\herbrandsfundamentaltheorem \\---~an encyclopedia article~---
\wirthnamenoindex
mbox{
% \sloppy \herbrandsfundamentaltheorem\ provides a constructive characterization of derivability in first-order predicate logic by means of sentential logic. Sometimes it is simply called ``\herbrand's Theorem\closequotecomma but the longer name is preferable as there are other important ``\herbrand\ theorems'' % (such as the {\herbrand--\ribet Theorem) and \herbrand\ himself called it\,{\em ``Th\'eor\`eme fondamental''. It was ranked by \citet{bernays-herbrand as follows: ``In its proof-theoretic form, \herbrandindex\herbrand's Theorem can be seen as the central theorem of predicate logic. It expresses the relation of predicate logic to propositional logic in a concise and felicitous form.'' And by \citet{heijenoort-logic-calculus-language: ``Let me say simply, in conclusion, that {\em\Begriffsschrift~\cite{begriffsschrift, \loewenheim's paper~\shortcite{loewenheim-1915, and Chapter\,\,5 of \herbrand's thesis \shortcite{herbrand-PhD are the three cornerstones of modern logic.'' \herbrandsfundamentaltheorem\ occurs in \litchapref 5 of his \PhDthesis\ \shortcite{herbrand-PhD ---~entitled {\em\herbrandPhDtitle~--- submitted by \herbrandname\ \herbrandlifetime\ in\,1929 at the University of Paris. \herbrandsfundamentaltheorem\ is, together with \goedel's incompleteness theorems and \gentzensHauptsatz, one of the most influential theorems of modern logic. Because of its complexity, \herbrandsfundamentaltheorem\ is typically fouled up in textbooks beyond all recognition. As we are convinced that there is still much more to learn for the future from this theorem than many logicians know, we will focus on the true message and its practical impact. This requires a certain amount of streamlining of \herbrand's work, which will be compensated by some remarks on the actual historical facts.
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\tableofcontents

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\section{Informal Introduction}
\vfill
\subsection{Validity in Sentential and in First-Order Logic}

The language of classical (\ie\ two-valued)
{\em sentential logic} (also called ``propositional logic'')
is \nolinebreak formed by {\em\myboolean\ operator symbols}
\\\LINEnomath
{---~~~~say conjunction \nlbmaths\tightund, \
disjunction \nlbmaths\tightoder, \
negation \nlbmath\neg~~~~---}
\\on {\em sentential variables}
(\ie\ nullary predicate symbols). \hskip.3em
For simplicity, but without loss of generality, 
we \nolinebreak will consider exactly the these three operators symbols 
as part of our language of sentential logic in this
article. \hskip.2em
Other operators will be considered just as syntactical sugar; \hskip.2em
for instance, material implication
\bigmaths{A\tightimplies B}{} will be considered a 
meta-level notion defined as \bigmaths{\neg A\tightoder B}.
The interpretation of the \myboolean\ operator symbols is fixed,
whereas the sentential variables range 
over the \myboolean\ values \TRUEpp\ and \FALSEpp. \hskip.3em
A \nolinebreak sentential formula is {\em valid}\/ \hskip.1em
if it evaluates to \nlbmath\TRUEpp\ 
for \nolinebreak all interpretations 
(\ie\ mappings to \myboolean\ values) 
of the sentential variables.

In a first step,
let us now add non-nullary {\em predicate symbols}, 
which take terms as arguments. 
{\em Terms}\/ are formed from {\em function symbols} and {\em variables}\/
over a non-empty {\em domain of individuals}, 
which has to be chosen by any interpretation and 
is a assumed to be well-determined and fixed in advance,
although it may be infinite. \hskip.2em
Such a {\em quantifier-free first-order formula}\/ 
is {\em valid}\/ \hskip.1em
if it evaluates to \nlbmath\TRUEpp\
for all interpretations of predicate symbols as functions from individuals 
to \myboolean\ values, of function symbols as functions from individuals to 
individuals, and of variables as individuals.

Note that this extension is not a substantial one, however, 
because the notion of validity does not change when 
we interpret the quantifier-free first-order formulas as sentential formulas, 
simply by considering the predicates together with their argument terms just
as names for atomic sentential variables.

In a second step,
we can add quantifiers such as ``\math{\forall\,}'' (``for all \ldots'') and 
``\math{\exists\,}''
(``there is a \ldots'') to bind variables. 
This means that formulas are now formed not only by applying \myboolean\ operators
to formulas, 
but also the \singulary\ operators ``\math{\forall x.}'' and 
\math{\exists x.}'', 
{\em binding}\/ an arbitrary variable symbol \nlbmaths x. \hskip.4em
%
Evaluation is now defined for these additional formula formations 
in the obvious way: \hskip.3em
\bigmath{\exists x\stopq A} 
(or else: \math{\forall x\stopq A}) \hskip.1em
evaluates to \TRUEpp\ if 
the single formula argument \nlbmath A 
\mbox{(its {\em scope})} \hskip.2em
evaluates to \TRUEpp\
for some interpretation of \nlbmath x 
(or else: for \nolinebreak all interpretations of \nlbmath x); \hskip.4em
otherwise it evaluates to \nlbmaths\FALSEpp.

With this second step we arrive at {\em first-order predicate logic}\/
(with function symbols).
This logic is crucially different from sentential logic,
because the testing of all domains of individuals becomes now 
unavoidable for determining validity of a formula in general. \hskip.3em
Even though it \nolinebreak actually suffices 
to check only one domain for each cardinality
(different from \nlbmaths 0, but including infinite ones), \hskip.2em
this cannot be executed effectively in general.
As noted above, 
however,
the domains do not matter 
if no quantifiers occur in a first-order formula.
\begin{definition}[Sentential Validity]\\
A first-order formula is {\em sententially valid}
\udiff\ it is quantifier-free and valid in sentential logic,
provided that we consider 
the predicates together with their argument terms just
as names for atomic sentential variables.
\getittotheright\qed\end{definition}
Note that a formula does not change its meaning if we replace a bound
variable with a fresh one.
For instance, there is not difference in validity between
\\\LINEmaths{\forall x\stopq\inparentheses
{\app{\ident{Human}}x\implies\app{\ident{Mortal}}x}}{}
\\and
\LINEmaths{\forall y\stopq\inparentheses
{\app{\ident{Human}}y\implies\app{\ident{Mortal}}y}},\mbox{~~~~~}
\\both expressing that ``all humans are mortal'' 
---~in a structure 
where the \singulary\ predicates {\ident{Human}} and {\ident{Mortal}}
have the obviously intended interpretation.
Note, however, that none of these equivalent formulas is
valid, because we also have to consider the 
structure where {\ident{Human}} is always \TRUEpp\ and {\ident{Mortal}}
is \FALSEpp, in which case the formula evaluates to \nlbmaths\FALSEpp.

Just like \herbrand,
we consider equality of formulas only up to renaming of bound variables.
Thus, we consider the two displayed formulas to be identical.

\begin{sloppypar}
A variable may also occur {\em free}\/ in a formula,
\ie\ not in the scope of any quantifier binding it. \hskip.2em
We \nolinebreak will, 
however,
tacitly consider only formulas where each occurrence of 
each variable is either free or otherwise bound by a unique quantifier.
This excludes ugly formulas such \nolinebreak as 
\mathnlb{\app{\ident{Human}}x
\hskip.06em\tightund\hskip.11em\exists x.\app{\ident{Mortal}}x}{,\,}
\mathnlb{\exists x.\app{\ident{Human}}x
\hskip.06em\tightund\hskip.11em
\exists x.\app{\ident{Mortal}}x}, or
\mathnlb{\forall x.\inparenthesestight{\app{\ident{Human}}x
\hskip.06em\tightund\hskip.11em\exists x.\app{\ident{Mortal}}x}}.
The bound variables of such formulas can always be renamed to obtain
nicer formulas in our restricted sense,
such as \bigmathnlb
{\app{\ident{Human}}x\und\exists z.\app{\ident{Mortal}}z}, 
\bigmathnlb{\exists x.\app{\ident{Human}}x\und
\exists z.\app{\ident{Mortal}}z}, and
\bigmathnlb{\forall x.\inparenthesestight
{\app{\ident{Human}}x\und\exists z.\app{\ident{Mortal}}z}}.
Both human comprehension and formal treatment become less difficult 
by this common syntactical restriction.\end{sloppypar}

\subsection{Calculi: Soundness, Completeness, Decidability}

To get a more constructive access to first-order predicate logic,\
validity has to be replaced with derivability in a calculus.
Such a calculus is {\em sound}\/ if we can derive only valid formulas with it,
and {\em complete}\/ if every valid formula can be derived with it.
Luckily, there are sound and complete calculi for first-order logic.

Let us consider formal derivation in a sound and complete calculus 
for first-order logic.
Then there are effective enumeration procedures that, in the limit, 
would produce an infinite list
of all derivable consequences.
This means that derivability in first-order logic is {\em semi-decidable}\/:
If we want to find out whether a first-order formula is derivable, 
we can start such an enumeration procedure
and say ``yes'' if our formula comes along.

Non-derivability in first-order logic, however, is not semi-decidable:
There cannot be an 
enumeration procedure for those first-order formulas which are not derivable.
\hskip.2em
In \nolinebreak other words, 
derivability is not {\em co-semi-decidable}.

A problem is {\em decidable}\/ if it is both semi- and co-semi-decidable. 
Therefore, the problem of derivability in first-order logic 
is not decidable:
There cannot be any effective procedure that,
for an arbitrary first-order formula as input,
always returns that one of the answers 
``yes'' and ``no'' that is correct \wrt\ its derivability.
Note that the problem of derivability in first-order logic 
is historically called the 
{\em Entscheidung\esi problem (in engerer Bedeutung)}, 
\ie\ the {\em decision problem (for first-order logic)});
\cfnlb\ 
\cite[\p,72\f]{grundzuege},
\cite
[\litnoteref{8.6}, \p\,8]{grundlagen-german-english-edition-volume-one-one}.

Sentential logic, however,
is decidable.

Therefore, it makes sense to characterize derivability in first-order logic
by a semi-decision procedure based on validity in sentential logic.
\pagebreak

\begin{remark}[Historical Correctness]\\
The notion of decidability was developed mainly after \herbrand's death.
The {\em Ent\-schei\-dung\esi problem}\/ was an open
problem during \herbrand's lifetime,
because the co-semi-undecidability was established only later by 
\citet{Church36b} and 
\citet{turing-entscheidungsproblem}.
\getittotheright\qed\end{remark}

% \notop\notop\halftop
\subsection{First Major Aspect of \herbrandsfundamentaltheorem}
% \notop\halftop\noindent
A major aspect of \herbrandsfundamentaltheorem\ is that it
provides a semi-decision procedure for first-order logic as follows:
For a given first-order formula \maths A,
this procedure produces
a list of quantifier-free first-order formulas
% \nlbmaths{F_1,F_2,F_3,\ldots}, 
\par\noindent\LINEmaths{
F^{\,\app{\termsofdepthnovars 1}F}\comma
F^{\,\app{\termsofdepthnovars 2}F}\comma
F^{\,\app{\termsofdepthnovars 3}F}\comma
\ldots}{}
\\[+.3ex]\noindent such that \math A is derivable in first order-logic
\ifandonlyif\ one of the formulas 
\nlbmath{F^{\,\app{\termsofdepthnovars i}F}} 
is sententially valid. \hskip.3em
We say that 
\math A has {\em\propertyC\ of order \nlbmath i}
\udiff\ \math{F^{\,\app{\termsofdepthnovars i}F}} is sententially valid.

% \notop\halftop
\subsection{Second Major Aspect of \herbrandsfundamentaltheorem}
% \notop\halftop\noindent
Another major aspect of \herbrandsfundamentaltheorem\ is
that in {\em\herbrand's {\it modus ponens}-free calculus}\/ for first-order logic
there is a linear derivation of \math A from 
\nlbmath{F^{\,\app{\termsofdepthnovars i}F}},
provided that \math A has \propertyC\ of order \nlbmaths i. \
A derivation is {\em linear}\/ if
---~seen as a tree~--- 
it \nolinebreak has no branching
because all inference rules have exactly one premise. \hskip.2em
In addition, 
this \nolinebreak derivation also has the so-called ``sub''-formula 
property \wrt\ \nlbmath A. \hskip.3em
Moreover,
contrary to all calculi that were invented before,
and similar to the calculi of \cite{gentzen},
\hskip.2em
\herbrand's {\it modus ponens}\/-free calculus
gives humans a good chance to actually find this linear derivation 
based on an informal proof. \hskip.3em
Furthermore, 
\herbrand's {\it modus ponens}\/-free calculus shows a great similarity with
today's approaches to automated theorem proving,
greater even than that of the well-known calculi of \cite{gentzen}.

% \pagebreak

% \notop\halftop
\subsection{Also a Completeness Theorem for \FirstOrder\ Logic}
% \notop\halftop\noindent
``\propertyC\hskip.07em'' is a name introduced in \cite{herbrand-PhD}.
Without a name, 
this property occurs already in \cite{loewenheim-1915}, \hskip.2em
% \pagebreak
where it is shown that a first-order formula 
% \nlbmath A 
is valid
\ifandonlyif\ it has \propertyC\ of order \nlbmaths i, \hskip.2em
for some positive natural number \nlbmath i 
\ ---~~which became famous as the \loewenheimskolemtheorem.

In his \PhDthesis,
\herbrandindex\herbrand\ also showed the equivalence of 
his own first-order calculi with those of the \hilbert\ school
\cite{grundlagen-german-english-edition-volume-one-two}
and the \PM~\cite{PM}. \
Therefore,
as a consequence of the \loewenheimskolemtheorem,
the completeness of all these calculi is an immediate
corollary of \herbrandsfundamentaltheorem. \

\herbrandindex\herbrand,
however, 
did not trust the notion of first-order validity.
As the first follower of \hilbert's {\em finitistic 
standpoint}\/ in proof theory in France,
\herbrandindex\herbrand\ was so radically finitistic that 
---~in the area of logic~--- 
he did not accept model theory or set theory at \nolinebreak all. \
And so \goedel\ proved the completeness of first-order logic first 
when he
submitted his thesis~\cite{goedel-completeness} in 1929, 
in the same year as \herbrandindex\herbrand, and the
theorem is now called {\em \goedel's Completeness Theorem}\/ 
in all textbooks on logic.%
\pagebreak

\begin{figure}[h]
\begin{center}%
\includegraphics
% [width=130mm,height=55mm,bb=20 20 575 308]%
% {LoewenheimSkolemHerbrand-FinalBridge.eps.gz}
% % %[width=120mm,height=55mm]
% % %[width=144mm,height=66mm]
% %\caption{\label{figure bridge}%
[width=130mm,height=55mm,bb=0 0 459 238]%
{LoewenheimSkolemHerbrand-FinalBridge.ps}
\begin{minipage}{\textwidthminustwocm}{\footnotesize\mbox{}\\[+1.7ex]%
Figure: 
The bridge of the \protect\loewenheimskolemtheorem\ and 
\protect\herbrandsfundamentaltheorem, 
based on the sentential \protect\propertyC\ standing firm in the river 
that divides the banks of valid and derivable formulas in the land of 
first-order predicate logic.\par}\end{minipage}
% }%
\notop\end{center}\end{figure}

\subsection{Constructiveness of \herbrandsfundamentaltheorem}

Why was the difference between the model-theoretic notion of validity
and the constructive notion of derivability in a sound and complete calculus
so crucial for \herbrand?
The reason,
of course, 
is the undecidability of first-order logic,
which essentially requires the non-constructive
use of actual infinities in the definition of validity. \hskip.2em
\hilbert's program in \nolinebreak logic 
---~best described in \cite{grundlagen-german-english-edition-volume-one-one}~---
was to show the consistency of such non-constructive methods in mathematics
by {\em finitistic methods}, 
\ie\ by methods that are even more restrictive than the intuitionistic
methods in mathematics following \brouwername.

\herbrand\ does not accept any
  model-theoretic semantics unless the models are finite. \ In this
  respect, \herbrand\ is more finitistic than \hilbert, who demanded
  finitism only for consistency proofs. 
\notop\halftop\begin{quote}
``\herbrand's negative view of set theory leads him to take,
on certain questions,
a \nolinebreak stricter attitude than \hilbert\ and his collaborators. \ 
He is more royalist than the king. \
\hilbert's metamathematics has as its main goal to establish the consistency 
of certain branches of mathematics and thus to justify them; \hskip.3em
there, one had to restrict himself to finitistic methods. \ 
But in logical investigations other than the consistency problem of
mathematical theories the 
\index{Hilbert!school}%
\hilbert\ school was ready to work with
set-theoretic notions.''\getittotheright
{%
\index{Heijenoort!Jean van}%
\cite[\p 118]{heijenoort-work-herbrand}}\notop\end{quote}
As a consequence of this ``royalist'' attitude,
\herbrand\ was very proud on the fact that his \fundamentaltheorem\ 
is perfectly constructive in the sense that its proof shows how
anything claimed can be constructed from anything given: \hskip.3em
From \math A, we can construct an arbitrary large part of 
the sequence 
\maths{F^{\,\app{\termsofdepthnovars 1}F},
F^{\,\app{\termsofdepthnovars 2}F},
F^{\,\app{\termsofdepthnovars 3}F},
\ldots}. \hskip.6em
From a derivation of \maths A, 
we \nolinebreak can compute a number \math i such that 
\math A has \propertyC\ of order \nlbmath i
(\ie\ such that \math{F^{\,\app{\termsofdepthnovars i}F}} 
 is sententially valid).
\hskip.4em
If \math A has \propertyC\ of order \nlbmaths i, \hskip.2em
we can construct a linear derivation of \nlbmath A from 
\nlbmath{F^{\,\app{\termsofdepthnovars i}F}}
\ ---~~provided that we are explicitly 
given \nlbmath i as a definite number.%
\pagebreak

\section{Formal Presentation}
\subsection{Basic Notions and Notation}

Before we can present \herbrandsfundamentaltheorem\ formally,
we have to provide 
some further notions and notation on first-order formulas and
several inference rules for first-order logic.
Note that we will partly use modern notions,
which did not exist at \herbrand's time.

If we want to focus on a certain position in a formula,
we write the formula as \maths{A[B]}. \
This means that \math B is a formula that occurs in the 
context \math{A[\ldots]} as a sub-formula at a certain fixed position,
which, however, is not explicitly given by the notation.
Then we \nolinebreak denote with \nlbmath{A[C]} the formula that results
from the formula \math{A[B]} by replacing the one occurrence
of \nlbmath B at the fixed position with the 
formula \nlbmath C.

We denote with \bigmaths{A
\{x_1\tight\mapsto t_1,\ldots,x_n\tight\mapsto t_n\}}{}
the result of replacing all occurrences of the distinct variables
\nlbmath{x_1,\ldots,x_n} in the formula \nlbmath A in parallel with the
terms \nlbmaths{t_1,\ldots,t_n}, respectively. \hskip.3em
Here, \maths{\{x_1\tight\mapsto t_1,\ldots,x_n\tight\mapsto t_n\}}{}
\nolinebreak is a notation for a {\em substitution},
\ie\ for a function from variables to terms.

The occurrence of a quantifier in a formula is {\em accessible}\/
if it is not in the scope of any other quantifier.
For instance, 
in the valid formula 
\\\LINEmaths{\forall x\stopq\exists y\stopq\inpit{x\tightprec y}
\oder\exists m\stopq\forall z\stopq\neg\inpit{m\tightprec z}}{}
\\on the binary predicate symbol \nlbmath\prec\ (with infix notation), \hskip.2em
the occurrences of the quantifiers 
\math{\forall x.} \nolinebreak and \nlbmath{\exists m.}
are the only accessible ones. \hskip.3em
Note that we assume the scopes of our quantifiers to be minimal
in the sense that the scope of \hskip.1em\math{\forall x.} in this formula
does not 
include the sub-formula \bigmathnlb{
\exists m\stopq\forall z\stopq\neg\inpit{m\tightprec z}}{}
---~~contrary to the formula 
\\\LINEmaths{\forall x\stopq\inparenthesestight{\exists y
\stopq\inpit{x\tightprec y}\oder
\exists m\stopq\forall z\stopq\neg\inpit{m\tightprec z}}},
\\where only the occurrence of \nolinebreak\hskip.1em\math{\forall x.} 
is accessible.

\citet{smullyan} classified reductive inference rules
---~and the inference rules of the \hilbert\ calculi 
we will consider here can all be seen as such if we read them
\mbox{bottom up~---}
into
\math\alpha~(sentential+non-branching),
\math\beta~(sentential+\underline branching),
\math\gamma, 
and \nlbmath\delta. \hskip.2em
According to this classification,
we introduce the following notion on quantifiers,
bearing in mind that \maths\tightund, 
\nlbmaths\tightoder, \nolinebreak and \nlbmath\neg\ \hskip.1em
are our only \myboolean\ operators.

The occurrence of a quantifier in formula is {\em\existentialoid} \hskip.1em
if it is of the form \nlbmath{\exists x.} 
and it is in the scope of an even number of
negation symbols,
or of the form \nlbmath{\forall x.} 
and in the scope
of an odd number of negation symbols;
otherwise the quantifier is {\em\universaloid}. \hskip.3em
(\Anexistentialoidquantifier\ turns up as \nlbmath\exists\ in a prenex form of
 the formula, 
 and \auniversaloidquantifier\ as \nlbmaths\forall.)

The occurrence of a variable in a formula is {\em\existentialoid}\/ \hskip.1em
if it is bound by \anexistentialoidquantifier; \hskip.2em
it is \universaloid\ if \nolinebreak it \nolinebreak is 
bound by \auniversaloidquantifier\ or free 
(\ie\ not bound by any quantifier).

\vfill\pagebreak
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{A Modern Version of \herbrand's {\it Modus Ponens}\/-Free Calculus}

Now we are prepared to understand the following three inference rules
which constitute a slightly improved version of 
\herbrand's {\it modus ponens}\/-free calculus in the style of 
\makeacitetofthree
{heijenoort-herbrand}
{heijenoort-modern-logic}
{heijenoort-work-herbrand}
and \makeacitetoftwo
{wirth-heijenoort}
{wirth-heijenoort-SEKI}.

Note that we may rename bound variables to satisfy the side conditions
of the inference rules, 
because we consider equality of formulas only up to renaming of bound
variables.

\par\yestop\noindent{\bf\Ruleofexistentialoidquantification:} \ 
\bigmaths{\begin{array}[c]{l}{A[H\{x\mapsto t\}]}
\\\hline
  {A[Q x\stopq H]}
\\\end{array}}{~}
where\begin{enumerate}\item
\math{Q x.} is an accessible \existentialoidquantifier\ of 
\nlbmath{A[Q x\stopq H]}, \ and\item the free variables of the term \nlbmath t 
\hskip.1em must not be bound by quantifiers in \nlbmaths H.%
\yestop\end{enumerate}

\begin{example}[Application of the \ruleofexistentialoidquantification]\label
{example Application of the rule of existentialoid quantification}%
\mbox{}
\\\noindent If the variable \math z does not occur free in the term \nlbmaths t,
we get the following two inference steps with identical premises
by application of the \ruleofexistentialoidquantification\
at two different positions:\begin{itemize}\item
\math{\begin{array}[c]{r c r}\inpit{t\tightprec t}
 &\oder
 &\neg\forall z\stopq\inpit{t\tightprec z}
\\\hline
  \inpit{t\tightprec t}
 &\oder
 &\exists x\stopq\neg\forall z\stopq\inpit{x\tightprec z}
\\\end{array}}{} \
via the meta-level substitution
\getittotheright{\maths{%\scriptstyle
\{\ \ \ \ A[\ldots]\ 
\mapsto\ \inpit{t\tightprec t}
\oder [\ldots]\comma\ \ \
H\ \mapsto\ \neg\forall z\stopq\inpit{x\tightprec z}
\comma\ \ \
Q\ \mapsto\ \exists
\ \ \ \ \}\majorfootroom\majorheadroom};\mbox{~~~~~\,}}\item
\maths{\begin{array}[c]{r c r}\inpit{t\tightprec t}
 &\oder
 &\neg\forall z\stopq\inpit{t\tightprec z}
\\\hline
  \inpit{t\tightprec t}
 &\oder
 &\neg\forall x\stopq\forall z\stopq\inpit{x\tightprec z}
\\\end{array}}{} \
via the meta-level substitution
\getittotheright{\maths{%\scriptstyle
\{\ \ \ \ A[\ldots]\ \mapsto\ 
\inpit{t\tightprec t}
\oder\,\neg[\ldots]
\comma\ \ \
H\ \mapsto\ \forall z\stopq\inpit{x\tightprec z}
\comma\ \ \
Q\ \mapsto\ \forall
\ \ \ \ \}\majorfootroom\majorheadroom}.}\qed\end{itemize}
\end{example}

\par\yestop\noindent
{\bf\Ruleofuniversaloidquantification:} \bigmaths{\begin{array}[c]{l}{A[H]}
  \\\hline
    {A[Q y\stopq H]}
  \\\end{array}}{~}
where\begin{enumerate}\item 
\math{Q y.} is an accessible \universaloidquantifier\
of \nlbmaths{A[Q y\stopq H]}, \ and\item
the variable \nlbmath y must not occur free 
in the context \nlbmath{A[\ldots]}.\majorfootroom\end{enumerate}

\par\yestop\noindent
{\bf\Ruleofsimplification:} \bigmaths{\begin{array}[c]{l}{A[H\circ H']}
\\\hline
  {A[H]}
\\\end{array}}{~} where\begin{enumerate}\item
``\math{\circ}'' stands for ``\tightoder'' if \math{[\ldots]} \nolinebreak
occurs in the scope of an even number of negation symbols 
in \nlbmath{A[\ldots]}, \ 
and for ``\tightund'' otherwise, 
and\item
\math{H'} is a variant of the sub-formula \nlbmath H \
(\ie, \math{H'} is \math H or % else
 can be obtained from \nlbmath H by the renaming of variables
bound in \nlbmath H).\majorfootroom\end{enumerate}
Moreover, the 
{\em generalized rule of \math\gamma-simplification} 
  is the sub-rule for the case that
  \math H \nolinebreak is of the form \bigmaths{Q y\stopq C}{}
  and \bigmaths{Q y.}{} is \anexistentialoidquantifier\
  of \bigmaths{A[Q y\stopq C]}.%
\pagebreak\par
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{remark}%
[Historic Version of \herbrand's {\it Modus Ponens}-Free Calculus]%
\label{remark historically correct calculus}%
\par\noindent\sloppy
The before-mentioned three rules 
are to be used for a modern presentation of \herbrand's
{\it modus ponens}\/-free calculus.
The historical {\it modus ponens}\/-free calculus of \herbrand\ 
had the generalized rule of simplification,
but
only the shallow rules of 
\mbox{``\math\gamma- and \math\delta-quantification\closequotecommanospace} \
compensated by the addition of the rules of passage.

\halftop\noindent
{\bf Rules of \math\gamma- and \math\delta-quantification}
% (just as the shallow version of the generalized rule of simplification)
result from our formalization of the generalized rules 
by restricting \nlbmath{A[\ldots]} to the empty context
\hskip.1em
(\ie\nolinebreak\ \math{A[Q x\stopq H]}, \eg, is just 
\nolinebreak\mbox{~\math{Q x\stopq H}).} 

\par\halftop\noindent{\bf Rules of Passage:} \
The following six \nolinebreak logical
  equivalences may be used for rewriting from left to right 
({\em prenex direction}\/) and from right to left 
({\em anti-prenex direction}\/), 
resulting in twelve \nolinebreak deep 
inference rules
(where \math B is a formula 
 in which the variable \nlbmath x does not occur free):
\\\noindent\LINEmath{\begin{array}{l c r@{~~~~}c@{~~~~}l}
       (1)
      & 
      &\neg\forall x\stopq A
      &\equivalent
      &\exists x\stopq \neg A
     \\(2)
      & 
      &\neg\exists x\stopq A
      &\equivalent
      &\forall x\stopq \neg A
     \\(3)%\footnotemark
      & 
      &\inpit{\forall x\stopq A}\nottight\oder B
      &\equivalent
      &\forall x\stopq \inpit{A\hskip.06em\tightoder B}
     \\(4)
      & 
      &B\nottight\oder\forall x\stopq A
      &\equivalent
      &\forall x\stopq \inpit{B\hskip.06em\tightoder A}
     \\(5)
      & 
      &\inpit{\exists x\stopq A}\nottight\oder B
      &\equivalent
      &\exists x\stopq \inpit{A\hskip.06em\tightoder B}
     \\(6)
      & 
      &B\nottight\oder\exists x\stopq A
      &\equivalent
      &\exists x\stopq \inpit{B\hskip.06em\tightoder A}
      \\\end{array}}%
\par\halftop\noindent
Note that \herbrand\ did not need rules of passage for conjunction
(besides the rules of passage for negation (1,\,2) and for disjunction 
(3,\,4,\,5,\,6)),
\hskip.2em
because he considered conjunction 
\bigmaths{A\hskip.09em\tightund\hskip.05em B}{} a
meta-level notion defined as \bigmaths
{\neg\inpit{\neg A\hskip.14em\tightoder\hskip.10em\neg B}}.

\herbrand\ needed his rules of passage
(in anti-prenex direction)
for the completeness of his historic {\it modus ponens}\/-free calculus
because the shallow rules of quantification
\mbox{---~contrary} to the generalized \mbox{ones~---}
cannot introduce quantifiers at 
non-top positions.

\herbrandindex\herbrand\ introduced these rules 
in \litsectref{2.2} of his \PhDthesis\
\cite{herbrand-PhD}. \
He \nolinebreak named 
the rules of \mbox{\math\gamma- and \math\delta-quantification}
``second'' and ``first rule of generalization'' 
\cite[\p\,74\f]{herbrand-logical-writings},
respectively 
({\it ``deuxi\`eme''}
 and 
 {\it ``premi\`ere r\`egle de g\'en\'eralisation''}
 \cite[\p\,68\f]{herbrand-ecrits-logiques}). \hskip.4em
%
At the same places, 
we also find 
% the (shallow) rule of simplification
% ({\it``r\`egle de simplification''}\/), 
% and 
the ``rules of passage'' 
({\it\mbox{``r\`egles} de passage''}\/\nolinebreak\hskip.2em\nolinebreak).
\hskip.4em
Finally, in \litsectref{5.6.A} of his \PhDThesis,
\herbrandindex\herbrand\ also introduces the generalized rule of simplification
\cite[\p\,175]{herbrand-logical-writings} 
({\it``r\`egle de simplification g\'en\'eralis\'ee''}
\cite[\p\,143]{herbrand-ecrits-logiques}).
\getittotheright\qed\end{remark}

\vfill\pagebreak
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{\propertyC}
\halftop\begin{definition}[Height of a Term, Champ Fini 
\nlbmath{\termsofdepth n F}]\label
{definition champs finis}\mbox{}
\par\noindent
We \nolinebreak use \nlbmath{\CARD t}
to denote the {\em height}\/ of a term \nlbmath t,
which is given by
%\\[-.9ex]
\par\noindent\LINEmaths{\CARD{\anonymousfpp{t_1}{t_{m}}}
  \nottight{\nottight{\nottight=}}1+\max\{0,\CARD{t_1},\ldots,\CARD{t_m}\}}.
\par\noindent For a positive natural number \nlbmath n
and a formula \nlbmath F,
as a finite substitute for a typically infinite, 
full term universe,
\herbrandindex\herbrand\ uses what he calls a 
{\em champ fini of order \nlbmaths n,} \hskip.1em
which we \nolinebreak will denote with 
\nlbmath{\termsofdepth n F}.  \ 
The terms of \nlbmath{\termsofdepth n F} 
are constructed from the symbols that occur free
in \nlbmath F: \
the function symbols, the constant symbols
(which we will tacitly subsume 
 under the function symbols in what follows), \hskip.1em
and the free variable symbols
(which can be seen as constant symbols here). \hskip.3em
Such a 
{\em champ fini}\/ differs from a full term universe in
containing only the terms \nlbmath t with \bigmaths{\CARD t\prec n}{\,.} \ 
\par\noindent 
So we have \bigmaths{\termsofdepth 1 F\tightequal\emptyset}. \hskip.2em
\par\noindent To guarantee \bigmaths
{\termsofdepth n F\tightnotequal\emptyset}{} \hskip.1em
for \bigmaths{n\succ 1},
in case that neither constants nor free variable symbols occur in \nlbmaths F,
\hskip.1em we will assume that a fresh constant symbol 
\nolinebreak ``\nlbmath\bullet\nolinebreak\hskip.02em\nolinebreak''
% , \hskip .2em the {\em lexicon}, 
(which does not occur elsewhere)
\hskip.1em is \nolinebreak
included in the term construction in addition to the free symbols of \nlbmath F.
\getittotheright\qed\end{definition}

\halftop\halftop\noindent\herbrand's definition of an expansion 
follows the traditional
idea that ---~for a {\em finite}\/ domain~--- universal (existential) 
quantification can be seen as a finite conjunction (disjunction) over the 
elements of the domain:
\begin{definition}[Expansion]\label
{definition sub-expansion}\sloppy\mbox{}\\Let \nlbmath{\mathcal T} be a 
finite set of terms. \
To simplify substitution,
let \nlbmath A be a formula whose bound variables do not occur in 
\nlbmaths{\mathcal T}.
\\The 
{\em expansion \nlbmath{A^{\mathcal T}} 
of \nlbmath A \wrt\ \nlbmath{\mathcal T}} \hskip.3em
is the formula given by the following recursive definition.
\\If \math A is quantifier-free formula,
then \bigmaths{A^{\mathcal T}:=A}.
Moreover:
\bigmaths{\inpit{\neg A_1}^{\mathcal T}:=\neg A_1^{\mathcal T}},
\\\bigmaths{\begin{array}[b]{l l l}\inpit{A_1\oder A_2}^{\mathcal T}
 &:=
 &A_1^{\mathcal T}\oder A_2^{\mathcal T},
\\\inpit{A_1\und A_2}^{\mathcal T}
 &:=
 &A_1^{\mathcal T}\und A_2^{\mathcal T},
\\\end{array}}{}
\bigmaths{\begin{array}[b]{l l l}\inpit{\exists x.\,A}^{\mathcal T}
 &:=
 &\bigvee_{t\in\mathcal T}\,A^{\mathcal T}\{x\tight\mapsto t\},
\\\inpit{\forall x.\,A}^{\mathcal T}
 &:=
 &\bigwedge_{t\in\mathcal T}\,A^{\mathcal T}\{x\tight\mapsto t\}.
\\\end{array}}{}
\getittotheright\qed\end{definition}
\begin{definition}[Outer \skolemizedForm]\label
{definition skolemized forms}\mbox{}\\
The {\em outer \skolemizedform\ of a formula \nlbmath A}\/ results from \nlbmath
A by removing every \universaloidquantifier\ and replacing its bound
variable \nlbmath x with \nlbmaths{\app{\forallvari x{}}{y_1,\ldots,y_m}}, \ 
where \math{\forallvari x{}} \nolinebreak is a fresh (``\skolem'') symbol
and \maths{y_1,\ldots,y_m}, in this order,
are the variables of the \math\gamma-quantifiers in
whose scope the \mbox{\math\delta-quantifier} occurs.
\getittotheright\qed\end{definition}

% \begin{definition}[\SententialTautology]\mbox{}\\
% A \firstorder\ formula is a {\em\sententialtautology}\/ if it
%     is quantifier-free and truth-functionally valid, provided its
%     atomic subformulas are read as atomic sentential variables.%
% % \footnotemark
% % \par\footnotetext
% % {Note that this notion is more
% %       restrictive than the following, 
% %     which is used by \herbrand\ in his thesis only initially, 
% %     but which is standard for the
% %       predicate calculi of the 
% % \hilbert\ school and the 
% % \PM; \ 
% % \cfnlb\ \cite[Supplement\,I\,D]{grundlagen-second-edition-volume-two}, \ 
% % \cite[*10]{PM}\@. \ %\\ 
% %       \math B \nolinebreak is \nolinebreak a
% %       {\em\substitutionalsententialtautology}\/
% %       \udiff\ there is a truth-functionally valid sentential formula \nlbmath
% %       A and a substitution \nlbmath\sigma\ mapping any sentential
% %       variable in \nlbmath A to a \firstorder\ formula such that \math
% %       B \nolinebreak is \nlbmath{A\sigma}. \ 
% %       %\\
% %       For example, both \bigmathnlb{\Pppp x{\oder}\neg\Pppp x}{} and
% %       \bigmathnlb{\exists x\stopq\Pppp x\nottight{\oder}\neg\exists
% %         x\stopq\Pppp x}{} are \substitutionalsententialtautologies,
% %       related to the truth-functionally 
% %       valid sentential formula \bigmathnlb{p{\oder}\neg
% %         p}, but only the first one is a \sententialtautology.}%
% \qed\end{definition}
  
\begin{definition}[\propertyC]\label
{definition properties C and C star}\mbox{}
\\Let \math A be a \firstorder\ formula. \ 
Let \math n be a positive natural number. \
\\Let \math F be
the outer \skolemizedform\ of \nlbmaths A.
\\\math A \nolinebreak
{\em has \propertyC\ of order \nlbmath 1}\/ \hskip.2em if \hskip.2em
\math F is a \sententialtautology.
\\For \bigmaths{n>1}, the formula \math A \nolinebreak
{\em has \propertyC\ of order \nlbmath n}\/ \hskip.2em if\\the 
expansion \nlbmath{F^{\,\app{\termsofdepthnovars n}F}} is a
\sententialtautology.
\getittotheright\qed\end{definition}

% \begin{corollary}\label{corollary sentential tautology}\\
% The following two are logically equivalent for every formula \nlbmaths A:
% \begin{enumerate}\notop\item
% \math A has \propertyC\ of order \nlbmaths 1.\noitem\item
% The outer \skolemizedform\ of 
% \nlbmath A is a \sententialtautology.\getittotheright\qed
% \end{enumerate}\end{corollary}

% \noindent
% Because all quantifiers in a \skolemizedform\ \nlbmath F 
% are \math\gamma-quantifiers,
% existential quantifiers occur only in the scope of an even number of 
% negation symbols 
% (and are expanded with disjunctions) 
% and universal quantifiers occur in the scope of an odd number
% (and are expanded with conjunctions). \
% Thus, 
% % every sub-expansion implies its extended expansion, and
% we get the following corollaries:
% \begin{corollary}\label{corollary sub-expansion} \
% If any sub-expansion of a \skolemizedform\ \nlbmath F 
% \wrt\ \nlbmath{\mathcal T}
% is a \sententialtautology,
% then \math{F^{\,\mathcal T}} is a \sententialtautology\ 
% as well.\end{corollary}
% \begin{corollary}\label{corollary sub-expansion two} \
% If any sub-expansion of the outer\/ \skolemizedform\ 
% \nlbmath F of the formula \nlbmath A
% \wrt\ \app{\termsofdepthnovars n}F is a \sententialtautology,
% then \math A has \propertyC\ 
% of order \nlbmath n.
% \getittotheright\qed\end{corollary}

% \halftop\halftop\noindent
% By using the idea of 
% \cororef{corollary sub-expansion} for the forward direction and
% by replacing all new terms with the same old constant or free variable 
% for the backward direction, 
% we \nolinebreak get:

% \begin{corollary}\label{corollary extend signature}\
% If\/ \math F is the outer \skolemizedform\ 
% of the formula \nlbmaths A,
% and if\, \math{\mathcal T'\!} is formed just as\/ \app{\termsofdepthnovars n}F,
% but over an extended set of 
% % functions
% %CP Mar25,2014:
% function 
% symbols,
% then \math A has \propertyC\ 
% of order \nlbmath n 
% \ifandonlyif\/ \math{F^{\,\mathcal T'}} is a \sententialtautology.%
% \pagebreak
% \getittotheright\qed\end{corollary}

\vfill\pagebreak

\subsection{The Theorem and its Lemmas}
\halftop\halftop
\begin{theorem}[\herbrandsfundamentaltheorem\ \`a la \heijenoort]%
\label{theorem herbrand fundamental two}%
\\Let\/ \math A be a \firstorder\ formula. 
The following two statements are logically equivalent. \hskip.3em
Moreover, 
we can construct a witness for each statement 
from a witness for the other one.\begin{enumerate}\notop\item[1.]%
There is a positive natural number \nlbmath n such that
\math A has \propertyC\ of order \nlbmaths n.\noitem\item[2.]\sloppy 
There\,is\,a\,\sententialtautology\ \nlbmaths B, 
and 
\\there\,is\,a\,derivation\,of \math A from \nlbmath B
that\,consists\,in\,applications\,of the generalized rules of
\\simplification, \hskip.2em
\mbox{\math\delta-quantification,} \hskip.2em
and\/ \mbox{\math\gamma-quantification} \hskip.2em
\\(and in the renaming of bound variables).
\getittotheright\qed\end{enumerate}\end{theorem}
\par\halftop\halftop\noindent
As we can decide \propertyC\ of order \nlbmath n \hskip.1em for 
\maths{n\tightequal 1}, \maths{n\tightequal 2},
\maths{n\tightequal 3}, \maths\ldots, \hskip.1em
\theoref{theorem herbrand fundamental two}
immediately provides us with a semi-decision procedure for derivability
(and, thus, by the \loewenheimskolemtheorem, also for validity)
of any \firstorder\ formula \nlbmath A given as input.

Note that the witnesses mentioned 
in \theoref{theorem herbrand fundamental two}
are, of course,
on the one hand, 
a \nolinebreak concrete representation of 
the natural number \nlbmaths n, \hskip.1em
and, on the other hand, concrete representations of 
the formula \nlbmath B and of
the derivation of \math A from \nlbmaths B.

To get some more information on the construction of these witnesses,
we have to decompose the equivalence of \theoref
{theorem herbrand fundamental two}
into the two implications found in the following two lemmas,
which constitute the theorem.

\begin{lemma}%[{\em Modus Ponens}\/ Elimination]
[From \propertyC\ to a Linear Derivation]
\label{lemma from C to yields a la heijenoort}%
\\\noindent
Let\/ \math A be a \firstorder\ formula. \
Let\/ \math F be the outer\/ \skolemizedform\ of \nlbmath A. \
Let\/ \math n be a positive natural number.
\\\noindent If\/ \math A has \propertyC\ of order \nlbmath n, 
then we can construct a derivation of \nlbmath A
of the following form, 
in which we read any term starting with a\/ \skolem\ function 
as an atomic variable:%
\\\noindent\begin{tabular}[b]{@{}l l}%
  \headroom
  {\bf Step\,1:} 
 &We \nolinebreak start with 
  the \sententialtautology\/ \nlbmaths{F^{\,\termsofdepth n F}\!}.
\\\headroom{\bf Step\,2:}
 &Then we may repeatedly apply the generalized rules of\/
%\\&\mbox{}\hskip.1em
  \math\delta- and \math\gamma-quanti\-fi\-cation.
\\\headroom{\bf Step\,3:}
 &Then we may repeatedly apply the generalized rule of\/
  \math\gamma-simplification.
\\\headroom{\bf Step\,4:}
 &Then we rename all bound \mbox{\math\delta-variables} 
  to obtain \nlbmath A.\\\end{tabular}\\[-2.5ex]\getittotheright\qed\end{lemma}
% \marginpar
% {\tiny It would be worthwhile to present this example here,
% but it would take five extra pages and exceed the size limit.}%
\par\halftop\halftop\noindent
The proof idea of \lemmref{lemma from C to yields a la heijenoort}
is to transform the computation of the expansion of the 
outer \skolemizedform\ into a 
reduction in \herbrand's {\it modus ponens}\/-free calculus.
In this transformation,
the reduction with the generalized rules of \math\gamma-simplification
and \mbox{\math\gamma-quantification} models the expansion,
and the renaming of bound \math\delta-variables 
to \skolem\ terms considered as variable names
models the \skolemization,
whereas the reduction with the generalized rules of
\math\delta-quantification just drops the \math\delta-quantifiers.
The critical task in this transformation is to find an appropriate total
order of the variable occurrences of the original expansion steps,
so that the side conditions of 
the resulting reductive applications of the inference rules are met. 

See \nolinebreak\cite[\litsectref 5]{wirth-heijenoort-SEKI}
for an elaborate, but easily conceivable example
for an application of a procedure that can actual construct
such a derivation.
That example also shows how to overcome the inefficiency of this procedure
and how to find a proof of a manageable size.

\pagebreak

\begin{lemma}[From a Linear Derivation to \propertyC]
\label{lemma from yields to C a la heijenoort}\sloppy\\\noindent
If there is a derivation of the \firstorder\ formula \nlbmath A 
from a \sententialtautology\
by applications of the 
generalized rules of simplification, and of\/
\math\gamma- and\/ \math\delta-quantification 
\mbox{(and renaming of bound variables),}
\\then \math A has \propertyC\ of order\/ 
\nlbmaths{\displaystyle1+\sum_{i=1}^m\CARD{t_i}},
\par\noindent
where \math{t_1,\ldots,t_m} are the instances for the meta-variable \nlbmath t
of the generalized rule of\/ \mbox{\math\gamma-quantification} in its \math m
applications in the derivation of \nlbmaths A.
\getittotheright\qed\end{lemma}

\halftop
\begin{remark}[Historical Version of \herbrandsfundamentaltheorem]
\par\noindent
As already explained in \remaref{remark historically correct calculus},
\herbrand's actual calculus was a bit different and had to take 
the detour via adding quantifiers on top level and then moving them in.
This seemed to admit a minor simplification by a 
detour via the prenex normal form.
To reduce a problem to problems of manageable size
({\it divide et impera}\/), \hskip.2em
the detour via prenex normal form was a leading standard 
at \herbrand's time. 
Meanwhile prenex normal form plays a lesser \role\
in the better logic courses
because of its crucial efficiency problems.
\par
In \nolinebreak \herbrand's case this problem turned out to be fatal for the
correctness of his proof:
\herbrand\ computed the upper bound for the order of 
\propertyC\ after application of the rules of passage much lower than
it actually is. This 
is well-documented under the name of \herbrandsfalselemma. \hskip.5em
\par
One correction of \herbrandsfalselemma\ 
is the one that we have presented in this article
and that consists in
adding 
---~to \herbrand's deep version of his inference rule of simplification~---
also the deep versions of his inference rules of quantification. \hskip.3em
Looking at the style in which the great mathematician \herbrandname\
organized his most creative work in logic we may say that,
if anybody had noticed this bug 
in \herbrand's proof during \herbrand's lifetime,
this correction would have been the most straightforward \mbox{bug fix} for him.
\hskip.3em
Moreover, 
this correction still is 
the most straightforward and most elegant one today. \hskip.3em
It was clearly outlined by \heijenoortname, \hskip.1em
but first sketched in publication in \cite{herbrand-handbook}, \hskip.3em
and first published with an explicit presentation 
in \cite{wirth-heijenoort}.\end{remark}

\halftop\halftop\halftop\halftop\section{Conclusion}
In this article
we have delivered what we consider the very essentials that any logician
should know on \herbrandsfundamentaltheorem, and we suggest 
\cite{wirth-heijenoort-SEKI} and \cite{SR--2009--01} for further reading on 
\herbrandsfundamentaltheorem, \herbrand's further work in logic,
and for a listing of further sources on the subject.
\vfill\pagebreak

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\small

\addcontentsline{toc}{section}{Acknowledgments}
\section*{Acknowledgments}
I would like to thank \anellisname\ \anellislifetime\ for all his kind help
for me and my work on \herbrandname\ and \heijenoortname.
\irving\ has made my life better and richer.
His death has left a gap in my life.


\nocite{writing-mathematics}
\addcontentsline{toc}{section}{References}
\bibliography{herbrandbib}


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\newcommand\Roundpsymbol       {\ident{Round}}
\newcommand\Quadrangularpsymbol{\ident{Quadrangular}}
\newcommand\Metpsymbol         {\ident{Met}}
\newcommand\Kissedpsymbol      {\ident{Kissed}}
\newcommand\Bishopsymbol       {\ident{Bishop}}
\newcommand\mindexsymbol[1]{\existsvari w{#1}}

\newcommand\nonnegpsymbol      {\ident{nonnegp}}
\newcommand\wellsymbol         {\ident{well}}
\newcommand\welltailsymbol     {\ident{welltail}}
\newcommand\varsymbol          {\ident{var}}
\newcommand\aritysymbol        {\ident{arity}}

\newcommand\whilesymbol        {\ident{while}}

\newcommand\nullsymbol         {\ident{null}}
\newcommand\hdsymbol           {\ident{hd}}
\newcommand\tlsymbol           {\ident{tl}}
\newcommand\insymbol           {\ident{in}}
\newcommand\applysymbol        {\ident{app}}
\newcommand\termsymbol         {\ident{term}}
\newcommand\russellsymbol      {\ident{russell}}
\newcommand\sqrtindordsymbol[1]{\ident{sqrtio#1}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%formulas
\mathcommand\tightim{\longrightarrow}
\mathcommand\im{\ \tightim\ }
\mathcommand\rs{\:\rulesugar\:\:}
\mathcommand\rulesugar{\longleftarrow}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mathcommand\doublepp[1]      {\doublesymbol   \beginargs{#1}\allargs}
\mathcommand\aritypp[1]      {\aritysymbol   \beginargs{#1}\allargs}
\mathcommand\lengthpp[1]      {\lengthsymbol   \beginargs{#1}\allargs}
\mathcommand\sizepp[1]      {\sizesymbol   \beginargs{#1}\allargs}
\mathcommand\wellpp[1]      {\wellsymbol   \beginargs{#1}\allargs}
\mathcommand\welltailpp[1]      {\welltailsymbol   \beginargs{#1}\allargs}
\mathcommand\varpp[1]      {\varsymbol   \beginargs{#1}\allargs}
\mathcommand\rempp[2]    {\remsymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\divpp[2]    {\divsymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\divrestpp[2]    {\divrestsymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\diveinspp[2]    {\diveinssymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\divzweipp[3]    {\divzweisymbol\beginargs{#1}\separgs{#2}
\separgs{#3}\allargs}
\mathcommand\diveinstailpp[4]    {\diveinstailsymbol\beginargs{#1}\separgs{#2}
\separgs{#3}\separgs{#4}\allargs}
\mathcommand\divzweitailpp[6]    {\divzweitailsymbol\beginargs{#1}\separgs{#2}
\separgs{#3}\separgs{#4}\separgs{#5}\separgs{#6}\allargs}
\mathcommand\mbppp[2]         {\mbpsymbol   \beginargs{#1}\separgs{#2}\allargs}
\mathcommand\revpp[1]     
{\revsymbol\beginargs{#1}\allargs}
\mathcommand\revppi[2]     
{\revsymbol^{#1}\beginargs{#2}\allargs}
\mathcommand\revtailpp[2]     
{\revtailsymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\revtailppi[3]
{\revtailsymbol^{#1}\beginargs{#2}\separgs{#3}\allargs}
\mathcommand\Permpp[2]     
{\Permsymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\Permppi[3]
{\Permsymbol^{#1}\beginargs{#2}\separgs{#3}\allargs}
\mathcommand\appendpp[2]      
{\appendsymbol \beginargs{#1}\separgs{#2}\allargs}
\mathcommand\appendppi[3]      
{\appendsymbol^{#1}\beginargs{#2}\separgs{#3}\allargs}
\mathcommand\Everypp[2]      
{\Everysymbol \beginargs{#1}\separgs{#2}\allargs}
\mathcommand\RExistspp[1]      
{\RExistssymbol \beginargs{#1}\allargs}
\mathcommand\appendlongpp[2]      
{\appendsymbol\left(\begin{array}{@{}l@{}}{#1}\separgs\\{#2}\end{array}\right)}
\mathcommand\cnspp[2]         {\cnssymbol   \beginargs{#1}\separgs{#2}\allargs}
\mathcommand\cnsppi[3]       {\cnssymbol^{#1}\beginargs{#2}\separgs{#3}\allargs}
\mathcommand\cnsindexpp[3]
{\cnsindexsymbol{#1}\beginargs{#2}\separgs{#3}\allargs}
\mathcommand\dlpp[2]          {\dlsymbol    \beginargs{#1}\separgs{#2}\allargs}
\mathcommand\dloncepp[2]      {\dloncesymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\dlonceppi[3]{\dloncesymbol^{#1}\beginargs{#2}\separgs{#3}\allargs}
\mathcommand\rcpp[2]          {\rcsymbol    \beginargs{#1}\separgs{#2}\allargs}
\mathcommand\brpp[2]          {\brsymbol    \beginargs{#1}\separgs{#2}\allargs}
\mathcommand\orpp[2]          {\orsymbol    \beginargs{#1}\separgs{#2}\allargs}
\mathcommand\andpp[2]         {\andsymbol   \beginargs{#1}\separgs{#2}\allargs}
\mathcommand\shortcnspp[2]    {\csymbol     \beginargs{#1}\separgs{#2}\allargs}
\mathcommand\tightshortcnspp[2]
{\csymbol\beginargs{#1}\tightsepargs{#2}\allargs}
\mathcommand\spp[1]           {\ssymbol     \beginargs{#1}\allargs}
\mathcommand\sppiterated[2]   {\ssymbol^{#1}\beginargs{#2}\allargs}
\mathcommand\sqrtindordpp[3]
                       {\sqrtindordsymbol{#1}\beginargs{#2}\separgs{#3}\allargs}
\mathcommand\ppp[1]           {\psymbol     \beginargs{#1}\allargs}
\mathcommand\pppiterated[2]   {\psymbol^{#1}\beginargs{#2}\allargs}
\mathcommand\zeropp           {\ident 0}
\mathcommand\Julietpp         {\ident{Juliet}}
\mathcommand\Romeopp          {\ident{Romeo}}
\mathcommand\Ipp              {\ident I}
\mathcommand\onepp            {\ident1}
\mathcommand\twopp            {\ident2}
\mathcommand\threepp          {\ident3}
\mathcommand\invertpp[1]      {\invertsymbol\beginargs{#1}\allargs}
\mathcommand\invpp[1]         {\invsymbol\beginargs{#1}\allargs}
\mathcommand\abspp[1]         {\abssymbol\beginargs{#1}\allargs}
\mathcommand\naturalspp[1]    {\naturalssymbol\beginargs{#1}\allargs}
\mathcommand\gensympp[1]      {\gensymsymbol\beginargs{#1}\allargs}
\mathcommand\nilpp            {\ident{nil}}
%\mathcommand\nilindexpp[1]    {\ident{nil}_{#1}}
\mathcommand\falsepp          {\ident{false}}
\mathcommand\truepp           {\ident{true}}
\mathcommand\FALSEpp          {\ident{FALSE}}
\mathcommand\TRUEpp           {\ident{TRUE}}
\mathcommand\UNDEFpp          {\ident{UNDEF}}
\mathcommand\weirdppp         {\ident{weirdp}}
\mathcommand\ambigppp         {\ident{ambigp}}
\mathcommand\zeropredicatepp[1]{\zeropredicatesymbol\beginargs{#1}\allargs}
\mathcommand\cppeins       [1]{\csymbol     \beginargs{#1}\allargs}
\mathcommand\cppzwei       [2]{\csymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\eppeins       [1]{\esymbol     \beginargs{#1}\allargs}
\mathcommand\fppeins       [1]{\fsymbol     \beginargs{#1}\allargs}
\mathcommand\fppeinsindex  [2]{\fsymbol_{#1}\beginargs{#2}\allargs}
\mathcommand\fppeinsiterated[2]{\fsymbol^{#1}\beginargs{#2}\allargs}
\mathcommand\gppeins       [1]{\gsymbol     \beginargs{#1}\allargs}
\mathcommand\gppzwei       [2]{\gsymbol     \beginargs{#1}\separgs{#2}\allargs}
\mathcommand\hppeins       [1]{\hsymbol     \beginargs{#1}\allargs}
\mathcommand\kppeins       [1]{\ksymbol     \beginargs{#1}\allargs}
\mathcommand\appzero          {\ident a}
\mathcommand\bppzero          {\ident b}
\mathcommand\cppzero          {\ident c}
\mathcommand\dppzero          {\ident d}
\mathcommand\eppzero          {\ident e}
\mathcommand\eqindexpp[3]{\eqindexsymbol{#1}\beginargs{#2}\separgs{#3}\allargs}
\mathcommand\ifthenindexpp
[3]{\ifthenindexsymbol{#1}\beginargs{#2}\separgs{#3}\allargs}
\mathcommand\ifthenelseindexpp
[4]{\ifthenelseindexsymbol{#1}\beginargs{#2}\separgs{#3}\separgs{#4}\allargs}
\mathcommand\eqpp[2]{\eqsymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\leqpp[2]{\leqsymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\lespp[2]{\lessymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\lexlespp[2]{\lexlessymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\lexlimlespp[3]
               {\lexlimlessymbol\beginargs{#1}\separgs{#2}\separgs{#3}\allargs}
\mathcommand\lexpp[3]{\lexsymbol\beginargs{#1}\separgs{#2}\separgs{#3}\allargs}
\mathcommand\ackpp[2]{\acksymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\switchpp[1]{\switchsymbol\beginargs{#1}\allargs}
\mathcommand\swatchpp[1]{\swatchsymbol\beginargs{#1}\allargs}
\mathcommand\whilepp[2]{\whilesymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\nullpp[1]{\nullsymbol\beginargs{#1}\allargs}
\mathcommand\nullppiterated[2]{\nullsymbol^{#1}\beginargs{#2}\allargs}
\mathcommand\hdpp[1]{\hdsymbol\beginargs{#1}\allargs}
\mathcommand\hdppiterated[2]{\hdsymbol^{#1}\beginargs{#2}\allargs}
\mathcommand\carpp[1]{\carsymbol\beginargs{#1}\allargs}
\mathcommand\cdrpp[1]{\cdrsymbol\beginargs{#1}\allargs}
\mathcommand\tlpp[1]{\tlsymbol\beginargs{#1}\allargs}
\mathcommand\tlppiterated[2]{\tlsymbol^{#1}\beginargs{#2}\allargs}
\mathcommand\inpp[2]{\insymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\inppiterated[3]{\insymbol^{#1}\beginargs{#2}\separgs{#3}\allargs}
\mathcommand\applypp[2]{\applysymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\applyppiterated
[3]{\applysymbol^{#1}\beginargs{#2}\separgs{#3}\allargs}
\mathcommand\termpp[2]{\termsymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\setpp[1]{\set\beginargs{#1}\allargs}
\mathcommand\russellpp[1]{\russellsymbol\beginargs{#1}\allargs}

\mathcommand\Tpp[6]{\turingmachinesymbol\beginargs{#1}\separgs{#2}\separgs
{#3}\separgs{#4}\separgs{#5}\separgs{#6}\allargs}
\mathcommand\Tppseven[7]{\turingmachinesymbol\beginargs{#1}\separgs{#2}\separgs
{#3}\separgs{#4}\separgs{#5}\separgs{#6}\separgs{#7}\allargs}
\mathcommand\foreverppp[6]{\ident{foreverp}\beginargs{#1}\separgs{#2}\separgs
{#3}\separgs{#4}\separgs{#5}\separgs{#6}\allargs}
\mathcommand\terminatesppp[6]{\terminatespsymbol\beginargs{#1}\separgs
{#2}\separgs{#3}\separgs{#4}\separgs{#5}\separgs{#6}\allargs}
\mathcommand\terminatespppone[1]{\terminatespsymbol \beginargs{#1}\allargs}
\mathcommand\statepp
[3]{\statesymbol\beginargs{#1}\separgs{#2}\separgs{#3}\allargs}
\mathcommand\tightstatepp
[3]{\statesymbol\beginargs{#1}\tightsepargs{#2}\tightsepargs{#3}\allargs}
\mathcommand\cmdpp
[3]{\cmdsymbol  \beginargs{#1}\separgs{#2}\separgs{#3}\allargs}
\mathcommand\tightcmdpp
[3]{\cmdsymbol  \beginargs{#1}\tightsepargs{#2}\tightsepargs{#3}\allargs}
\mathcommand\stoppp           {\ident{stop}}
\mathcommand\leftpp           {\ident{left}}
\mathcommand\rightpp          {\ident{right}}
\mathcommand\nthpp         [2]{\nthsymbol  \beginargs{#1}\separgs{#2}\allargs}
\mathcommand\pppp          [1]{\ppsymbol\beginargs{#1}            \allargs}
\mathcommand\qppp          [2]{\qpsymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\Eppp          [1]{\Epsymbol\beginargs{#1}            \allargs}
\mathcommand\Epppzwei      [2]{\Epsymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\Pppp          [1]{\Ppsymbol\beginargs{#1}            \allargs}
\mathcommand\Ppppeinsindex [2]{\Ppsymbol_{#1}\beginargs{#2}\allargs}
\mathcommand\Ppppdrei      
[3]{\Ppsymbol\beginargs{#1}\separgs{#2}\separgs{#3}\allargs}
\mathcommand\Ppppvier
[4]{\Ppsymbol\beginargs{#1}\separgs{#2}\separgs{#3}\separgs{#4}\allargs}
\mathcommand\Qppp          [2]{\Qpsymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\Qpppeins      [1]{\Qpsymbol\beginargs{#1}\allargs}
\mathcommand\Qpppeinsindex [2]{\Qpsymbol_{#1}\beginargs{#2}\allargs}
\mathcommand\Qpppdrei      
[3]{\Qpsymbol\beginargs{#1}\separgs{#2}\separgs{#3}\allargs}
\mathcommand\Fatherpp      [2]{\Fathersymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\Marriespp     [2]{\Marriessymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\Lovespp       [2]{\Lovessymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\StolenBypp    [2]
{\StolenBysymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\Humanpp       [1]{\Humansymbol\beginargs{#1}\allargs}
\mathcommand\Evenpp        [1]{\Evensymbol\beginargs{#1}\allargs}
\mathcommand\Evenppi       [2]{\Evensymbol^{#1}\beginargs{#2}\allargs}
\mathcommand\Oddpp         [1]{\Oddsymbol\beginargs{#1}\allargs}
\mathcommand\Primepp       [1]{\Primesymbol\beginargs{#1}\allargs}
\mathcommand\EveryPairpp  [2]{\EveryPairsymbol\beginargs{#1}\separgs
{#2}\allargs}
\mathcommand\mindexppeins  [2]{\mindexsymbol{#1}\beginargs{#2}\allargs}
\mathcommand\Givepp        [3]{\Givesymbol
\beginargs{#1}\separgs{#2}\separgs{#3}\allargs}
\mathcommand\mindexppzwei  [3]{\mindexsymbol
{#1}\beginargs{#2}\separgs{#3}\allargs}
\mathcommand\mindexppdrei  [4]{\mindexsymbol
{#1}\beginargs{#2}\separgs{#3}\separgs{#4}\allargs}

\mathcommand\nonnegppp     [1]{\nonnegpsymbol\beginargs{#1}\allargs}

\mathcommand\anonymouscsymbol{c}
\mathcommand\anonymouscindexsymbol[1]{\anonymouscsymbol_{#1}}
\mathcommand\anonymousfsymbol{f}
\mathcommand\anonymouscpp
[2]{\anonymouscsymbol\beginargs{#1}\separgs\ldots\separgs{#2}\allargs}
\mathcommand\anonymouscindexpp
[3]{\anonymouscindexsymbol{#1}\beginargs{#2}\separgs\ldots\separgs{#3}\allargs}
\mathcommand\anonymousfpp
[2]{\anonymousfsymbol\beginargs{#1}\separgs\ldots\separgs{#2}\allargs}
\mathcommand\coerceindexpp[3]{[#3]_{#1}^{#2}}

\mathcommand\Elephantppp    [1]{\Elephantpsymbol\beginargs{#1}\allargs}
\mathcommand\Flowerppp      [1]{\Flowerpsymbol  \beginargs{#1}\allargs}
\mathcommand\Bicycleppp     [1]{\Bicyclepsymbol \beginargs{#1}\allargs}
\mathcommand\Germanppp      [1]{\Germanpsymbol  \beginargs{#1}\allargs}
\mathcommand\Hugeppp        [1]{\Hugepsymbol    \beginargs{#1}\allargs}
\mathcommand\Animalppp      [1]{\Animalpsymbol  \beginargs{#1}\allargs}
\mathcommand\Maleppp        [1]{\Malepsymbol    \beginargs{#1}\allargs}
\mathcommand\Boyppp         [1]{\Boypsymbol     \beginargs{#1}\allargs}
\mathcommand\Girlppp        [1]{\Girlpsymbol    \beginargs{#1}\allargs}
\mathcommand\Femaleppp      [1]{\Femalepsymbol  \beginargs{#1}\allargs}
\mathcommand\Roundppp       [1]{\Roundpsymbol   \beginargs{#1}\allargs}
\mathcommand\Bishoppp       [1]{\Bishopsymbol   \beginargs{#1}\allargs}
\mathcommand\Quadrangularppp[1]{\Quadrangularpsymbol  \beginargs{#1}\allargs}
\mathcommand\Kissedppp[2]{\Kissedpsymbol\beginargs{#1}\separgs{#2}\allargs}
\mathcommand\Metppp[2]   {\Metpsymbol   \beginargs{#1}\separgs{#2}\allargs}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%GENERAL STUFF
\newcommand\bound     {{\rm bound}}
\newcommand\free      {{\rm free}}

\mathcommand\Vtripleindex[3]{\V\!_{{#1},\,{#2},\,{#3}}}
\mathcommand\Vdoubleindex[2]{\V\!_{{#1},\,{#2}}}
\mathcommand\Vsingleindex[1]{\V\!_{{#1}}}

\newcommand\exrelation{\mbox{\math\Gammaoffont-}relation}
\newcommand\unrelation{\mbox{\math\Deltaoffont-}relation}
\mathcommand\Erel[1]{\Gammaoffont\!_{#1}}
\mathcommand\Urel[1]{\Deltaoffont_{#1}}

\newcommand\exRsub  {\math R-sub\-sti\-tu\-tion  on \nolinebreak\Vsome}
\newcommand\aexRsub {an \math R-sub\-sti\-tu\-tion  on \nolinebreak\Vsome}
\newcommand\exRsubs {\math R-sub\-sti\-tu\-tions on \nolinebreak\Vsome}
\newcommand\ExRSubs {\math R-Sub\-sti\-tu\-tions on \nolinebreak\Vsome}
\newcommand\Rsub    {\math R-sub\-sti\-tu\-tion}
\newcommand\aRsub   {an \math R-sub\-sti\-tu\-tion}
\newcommand\RSub    {\math R-Sub\-sti\-tu\-tion}
\newcommand\Rsubs   {\math R-sub\-sti\-tu\-tions}
\newcommand\RSubs   {\math R-Sub\-sti\-tu\-tions}
\newcommand\aRprimesub{an \math{R'}-sub\-sti\-tu\-tion}
\newcommand\aexRprimesub{\aRprimesub\ on \nolinebreak\Vsome}
\newcommand\exemptysetsub
{\math\emptyset-sub\-sti\-tu\-tion  on \nolinebreak\Vsome}

\newcommand\quasiexRsubs
{\Rsubs\ on \nolinebreak\math{\Vsome\cup\Vsall}}
\newcommand\aquasiexRsub
{\aRsub\ on \nolinebreak\math{\Vsome\cup\Vsall}}
\newcommand\isquasiexistential{is a substitution on \nlbmath{\Vsome\cup\Vsall}}

%\newcommand\sentencewithquasi
%{For an \Rsub\ \nlbmath{\sigma}\ on \math{\Vsome\,\opt{\cup\,\Vsall}}}
\newcommand\aexRsuboptquasi
{\aRsub\ on \nolinebreak\math{\Vsome\,\opt{\cup\,\Vsall}}}

% \newcommand\strongexRsub {existential \math R-sub\-sti\-tu\-tion}
% \newcommand\astrongexRsub{an \strongexRsub}
% \newcommand\strongexRprimesub{existential \math{R'}-sub\-sti\-tu\-tion}
% \newcommand\astrongexRprimesub{an \strongexRprimesub}
% \newcommand\strongexemptysetsub{existential \math\emptyset-sub\-sti\-tu\-tion}
% \newcommand\astrongexemptysetsub{an \strongexRemptysetsub}

\newcommand\strongsigmaupdate{\math\sigma-update}

\newcommand\strongexvalof[2]{\pair{#1}{#2}-valu\-a\-tion}
\newcommand\astrongexvalof[2]{an\/ \strongexvalof{#1}{#2}}
\newcommand\strongexRval {\strongexvalof\salgebra R}
\newcommand\StrongexRVal {\pair\salgebra R-Valu\-a\-tion}
\newcommand\strongexRvals{\pair\salgebra R-valu\-a\-tions}
\newcommand\StrongexRVals{\pair\salgebra R-Valu\-a\-tions}
\newcommand\astrongexRval{an \strongexRval}
\newcommand\strongexRprimeval{\pair\salgebra{R'}-valu\-a\-tion}
\newcommand\astrongexRprimeval{an\/ \strongexRprimeval}

\newcommand\cc{choice-condition}
\newcommand\CC{Choice-Condition}
\newcommand\Cc{Choice-condition}
\newcommand\vc{vari\-able-con\-di\-tion}
\newcommand\VC{Vari\-able-Con\-di\-tion}
\newcommand\Vc{Vari\-able-con\-di\-tion}
\newcommand\semanticobject{\mbox{\math\Sigmaoffont-}struc\-ture}

\newcommand\validity[2]{\pair{#1}{#2}-validity}
\newcommand\Validity[2]{\pair{#1}{#2}-Validity}
\newcommand\valid[2]{\pair{#1}{#2}-valid}
\newcommand\validstrongtrip[3]{\trip{#1}{#2}{#3}-valid}
\newcommand\validitystrongtrip[3]{\trip{#1}{#2}{#3}-validity}

\newcommand\stronglyreduces[3]{\pair{#1}{#2}-reduces}
\mathcommand\theRprimefromstrongtoweak{
  \inparenthesesinlinetight{
     \domres\id{\Vwall\cup\Vsome\setminus\RAN\varsigma}
     \nottight{\nottight\uplus}
     \reverserelation\varsigma
  }
  \nottight{\circ}
  \ranres
    {\transclosureinline R}
    {\Vwall\cup\Vsome\setminus\RAN\varsigma}
  \nottight{\nottight{\nottight{\uplus}}}
  \Vsome\tighttimes\Vsall
}

\mathcommand\deltaminus{\delta^-}
\mathcommand\deltaplus{\delta^+}
\mathcommand\deltaplusplus{\delta^{+^+}}
\mathcommand\deltastar{\delta^*}
\mathcommand\deltastarstar{\delta^{*^*}}
\newcommand\varihelper[1]{free \discretionary
{\mbox{\math{#1}-vari-}}{\mbox{able}}{\mbox{\math{#1}-variable}}}
\newcommand\Varihelper[1]{Free \discretionary
{\mbox{\math{#1}-vari-}}{\mbox{able}}{\mbox{\math{#1}-variable}}}
\newcommand\fev {\varihelper\gamma}
\newcommand\fuv {\varihelper\delta}
\newcommand\wfuv{\varihelper{\delta^-}}
\newcommand\sfuv{\varihelper{\delta^+}}
\newcommand\Fev {\Varihelper\gamma}
\newcommand\Fuv {\Varihelper\delta}
\newcommand\Wfuv{\Varihelper{\delta^-}}
\newcommand\Sfuv{\Varihelper{\delta^+}}
\newcommand\FUV {Free \math{\delta  }-Variable}
\newcommand\SFUV {Free \math{\delta^+}-Variable}

\mathcommand\Vall     {\Vsingleindex\indexdelta         }
\mathcommand\Vwall    {\Vsingleindex\indexdeltaminu     }
\mathcommand\Vsall    {\Vsingleindex\indexdeltaplus     }
\mathcommand\Vgsome   {\Vsingleindex\indexgammaplus     }
\mathcommand\Vsome    {\Vsingleindex\indexgamma         }
\mathcommand\Vfree    {\Vsingleindex\indexfree          }
\mathcommand\Vbound   {\Vsingleindex\indexbound         }
\mathcommand\Vsomesall{\Vsingleindex\indexgammadeltaplus}

\mathapplycommand\VARall      {\VARsingleindex\indexdelta         }
\mathapplycommand\VARwall     {\VARsingleindex\indexdeltaminu     }
\mathapplycommand\VARsall     {\VARsingleindex\indexdeltaplus     }
\mathapplycommand\VARgsome    {\VARsingleindex\indexgammaplus     }
\mathapplycommand\VARsome     {\VARsingleindex\indexgamma         }
\mathapplycommand\VARfree     {\VARsingleindex\indexfree          }
\mathapplycommand\VARbound    {\VARsingleindex\indexbound         }
\mathapplycommand\VARsomesall {\VARsingleindex\indexgammadeltaplus}
\mathcommand\displayVARsall[1]{\VARsingleindex\indexdeltaplus
\!\!\!\:\left(\begin{array}{@{}c@{}}#1\end{array}\right)}

\mathcommand\rigidvari     [2]{#1_{#2}^\indexgammadeltaplus}
\mathcommand\existsvari    [2]{#1_{#2}^\indexgamma    }
\mathcommand\forallvari    [2]{#1_{#2}^\indexdelta    }
\mathcommand\freevari      [2]{#1_{#2}^\indexfree     }
\mathcommand\wforallvari   [2]{#1_{#2}^\indexdeltaminu}
\mathcommand\sforallvari   [2]{#1_{#2}^\indexdeltaplus}
\mathcommand\gexistsvari   [2]{#1_{#2}^\indexgammaplus}
\mathcommand\boundvari     [2]{#1_{#2}}
\mathcommand\vari          [2]{#1_{#2}}
\mathcommand\wforallvarilow[2]{#1_{#2}^
{\raisebox{-.82ex}{\math\indexdeltaminu}}}

\newcommand\indexhelper[1]{{\scriptscriptstyle#1\:\!\!}}
\newcommand\indexdeltaplus
{\indexhelper{\delta^{\raisebox{-.17ex}{\fvesf\hskip-0.14em +}}}}
\newcommand\indexdeltaminu
{\indexhelper{\delta^{\mbox{\fvesf\hskip-0.14em\rule[.2ex]{.7em}{.15ex}}}}}
\newcommand\indexgammaplus
{\indexhelper{\gamma^{\mbox{\fvesf\hskip-0.14em +}}}}
\newcommand\indexgammadeltaplus
{\indexhelper{\gamma\delta^{\raisebox{-.17ex}{\fvesf\hskip-0.14em +}}}}

\newcommand\indexdelta{\indexhelper\delta}
\newcommand\indexgamma{\indexhelper\gamma}
\newcommand\indexfree
{{\scriptscriptstyle\free}}
\newcommand\indexbound
{{\scriptscriptstyle\bound}}

\newcommand\Wellfsymb{\ident{Wellf}}
\mathapplycommand\Wellfpp{\Wellfsymb}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%OBSOLETE STUFF
%%variables
%\mathcommand\x {x\:}\mathcommand\y {y\:}\mathcommand\z {z\:}
%\mathcommand\el{l\:}\mathcommand\k {k\:}\mathcommand\be{b\:}
%\mathcommand\h {h\:}
%%constants
%\mathcommand\zero{\ident{0}\:}\mathcommand\nil{\ident{nil}\:}
%\mathcommand\strangelist{\mbox{\ident{strange--list}}\:}
%\mathcommand\true {\ident{true}\:}\mathcommand\false{\ident{false}\:}
%%functions
%\mathcommand\f  {\ident{f}\:}\mathcommand\s  {\ident{s}\:}
%\mathcommand\cns{\ident{cons}\:}\mathcommand\car{\ident{car}\:}
%\mathcommand\cdr{\ident{cdr}\:}\mathcommand\identminus{\minussymbol\:}
%\mathcommand\mbp{\mbpsymbol\:}\mathcommand\plus{\plussymbol\:}
%\mathcommand\dl {\ident{dl} \:}\mathcommand\ssp{\ident{ssp}\:}
%%literals
%\mathcommand\eqcolon{\boldequal\:}\mathcommand\necolon{\boldunequal\:}

headerhot.tex
\def\subsubsubsection{\paragraph}
\catcode`\@=11
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\font\sixsf  = cmss10 scaled 600
\font\fvesf  = cmss10 scaled 500
%\font\sevsf  = cmss10 scaled 700
\font\egtsf  = cmss10 scaled 800
%\font\twfvit  = cmti10   \@magscale5 % text italic

\def\xiipt{\textfont\z@\twlrm 
  \scriptfont\z@\egtrm \scriptscriptfont\z@\sixrm
\textfont\@ne\twlmi \scriptfont\@ne\egtmi \scriptscriptfont\@ne\sixmi
\textfont\tw@\twlsy \scriptfont\tw@\egtsy \scriptscriptfont\tw@\sixsy
\textfont\thr@@\tenex \scriptfont\thr@@\tenex \scriptscriptfont\thr@@\tenex
\def\unboldmath{\everymath{}\everydisplay{}\@nomath\unboldmath
          \textfont\@ne\twlmi 
          \textfont\tw@\twlsy \textfont\lyfam\twlly
          \@boldfalse}\@boldfalse
\def\boldmath{\@ifundefined{twlmib}{\global\font\twlmib\@mbi\@magscale1\global
        \font\twlsyb\@mbsy \@magscale1\global\font
         \twllyb\@lasyb\@magscale1\relax\@addfontinfo\@xiipt
              {\def\boldmath{\everymath
                {\mit}\everydisplay{\mit}\@prtct\@nomathbold
                \textfont\@ne\twlmib \textfont\tw@\twlsyb 
                \textfont\lyfam\twllyb\@prtct\@boldtrue}}}{}\@xiipt\boldmath}%
\def\prm{\fam\z@\twlrm}%
\def\pit{\fam\itfam\twlit}\textfont\itfam\twlit \scriptfont\itfam\egtit
   \scriptscriptfont\itfam\sevit
\def\psl{\fam\slfam\twlsl}\textfont\slfam\twlsl 
     \scriptfont\slfam\tensl \scriptscriptfont\slfam\tensl
\def\pbf{\fam\bffam\twlbf}\textfont\bffam\twlbf 
   \scriptfont\bffam\ninbf \scriptscriptfont\bffam\ninbf 
\def\ptt{\fam\ttfam\twltt}\textfont\ttfam\twltt
   \scriptfont\ttfam\nintt \scriptscriptfont\ttfam\nintt 
\def\psf{\fam\sffam\twlsf}\textfont\sffam\twlsf
    \scriptfont\sffam\egtsf \scriptscriptfont\sffam\sixsf
\def\psc{\@getfont\psc\scfam\@xiipt{\@mcsc\@magscale1}}%
\def\ly{\fam\lyfam\twlly}\textfont\lyfam\twlly 
   \scriptfont\lyfam\egtly \scriptscriptfont\lyfam\sixly
 \@setstrut \rm}

\def\xxvpt{\textfont\z@\twfvrm 
  \scriptfont\z@\twtyrm \scriptscriptfont\z@\svtnrm
\textfont\@ne\twtymi \scriptfont\@ne\twtymi \scriptscriptfont\@ne\svtnmi
\textfont\tw@\twtysy \scriptfont\tw@\twtysy \scriptscriptfont\tw@\svtnsy
\textfont\thr@@\tenex \scriptfont\thr@@\tenex \scriptscriptfont\thr@@\tenex
\def\unboldmath{\everymath{}\everydisplay{}\@nomath\unboldmath
        \textfont\@ne\twtymi \textfont\tw@\twtysy \textfont\lyfam\twtyly
        \@boldfalse}\@boldfalse
\def\boldmath{\@subfont\boldmath\unboldmath}%
\def\prm{\fam\z@\twfvrm}%
\def\pit{\fam\z@\twfvit}%
\def\psl{\@subfont\sl\rm}%
\def\pbf{\@getfont\pbf\bffam\@xxvpt{cmbx10\@magscale5}}%
\def\ptt{\@subfont\tt\rm}%
\def\psf{\@subfont\sf\rm}%
\def\psc{\@subfont\sc\rm}%
\def\ly{\fam\lyfam\twtyly}\textfont\lyfam\twtyly 
   \scriptfont\lyfam\twtyly \scriptscriptfont\lyfam\svtnly 
\@setstrut \rm}

\catcode`\@=12


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% SUPERCOMMANDS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% The following redefines the latex macro \math not because 
% \math makes trouble but rather because I dont like it
\long\def\math#1{\relax\ifmmode{#1}\else$#1 $\fi}
%                                          ^ 
% This blank is necessary because otherwise \math{} may expand to $$
% which is different from $ $ insofar as it starts a displaymath environment 
\long\def\nomath#1{\relax\ifmmode\mbox{#1}\else{#1}\fi}
\newcommand\nlbmath[1]{\nolinebreak\math{#1}}
\newcommand\maths[2]{\math{#1#2}}
\newcommand\nlbmaths[2]{\nolinebreak\math{#1#2}}
%The fol. defines \mathcommand to work like \newcommand with the exception of 
%switching to math-mode iff the command is not called in math-mode.
%\remathcommand is like \renewcommand.

\catcode`\@=11

\long\def\@reargdefmath#1[#2]#3{\@reargdef#1[#2]{\math{#3}}}

\long\def\@argdefmath#1[#2]#3{\@ifdefinable #1{\@reargdefmath#1[#2]{#3}}}

\def\mathcommand#1{\@ifnextchar [{\@argdefmath#1}{\@argdefmath#1[0]}}

\def\remathcommand#1{\edef\@tempa{\expandafter\@cdr\string
  #1\@nil}\@ifundefined{\@tempa}{\@latexerr{\string#1\space undefined}\@ehc
    }{}\@ifnextchar [{\@reargdefmath#1}{\@reargdefmath#1[0]}}

\catcode`\@=12

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\mathapplycommand      
#1#2{\mathcommand{#1}[1]{{#2}({##1})}}
\def\mathdoubleapplycommand
#1#2{\mathcommand{#1}[2]{{#2}({##1},{##2})}}
\def\mathtripleapplycommand
#1#2{\mathcommand{#1}[3]{{#2}({##1},{##2},{##3})}}
%example: \mathapplycommand\foo{\rm rubbish}
%         \foo{x} 
%produces:
%         rubbish(x)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\let\mathoverline=\overline
\remathcommand\overline[1]{\mathoverline{#1}}
% This makes \overline more intelligent, namely switching into math-mode
% if use in text-mode

\newcommand\mycomment[1]{{\iffalse{#1}\fi}}
% The argument of \comment is completely ignored

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Typesetting basics (lengths, struts) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% \setlength{\parindent}{2.0em}
\newlength{\disp}
\setlength{\disp}{\textwidth}
\addtolength{\disp}{-2.0\parindent}

\newlength{\textwidthminustwomm}
\setlength{\textwidthminustwomm}{\textwidth}
\addtolength{\textwidthminustwomm}{-0.2cm}

\newlength{\textwidthminushalfcm}
\setlength{\textwidthminushalfcm}{\textwidth}
\addtolength{\textwidthminushalfcm}{-0.5cm}

\newlength{\textwidthminusonecm}
\setlength{\textwidthminusonecm}{\textwidth}
\addtolength{\textwidthminusonecm}{-1.0cm}

\newlength{\textwidthminustwocm}
\setlength{\textwidthminustwocm}{\textwidth}
\addtolength{\textwidthminustwocm}{-2.0cm}

\newlength{\textwidthminusfourcm}
\setlength{\textwidthminusfourcm}{\textwidthminustwocm}
\addtolength{\textwidthminusfourcm}{-2.0cm}

\newlength{\textwidthminussixcm}
\setlength{\textwidthminussixcm}{\textwidth}
\addtolength{\textwidthminussixcm}{-6.0cm}

\newcommand\notop   {\vspace{-1.0\topsep}}
\newcommand\yestop  {\vspace{\topsep}}
\newcommand\halftop {\vspace{0.5\topsep}}
\newcommand\eighthtop{\vspace{0.125\topsep}}
\newcommand\ohyestop{\vspace*{\topsep}}
\newcommand\noitem  {\vspace{-1.0\itemsep}}
\newcommand\yesitem {\vspace{\itemsep}}

\newcommand\schweinerei{
\topsep 4pt plus 1pt minus 2pt
\partopsep 2pt plus 1pt minus 1pt
\renewcommand{\baselinestretch}{0.96}
\hfuzz=4pt}



\newcommand\bigmath[1]{\ \math{#1}\ }
\newcommand\bigmaths[2]{\ \math{#1}#2\ }
\newcommand\mathnlb[2]{\mbox{\math{#1}#2}}
\newcommand\bigmathnlb[2]{\ \mathnlb{#1}{#2}\ }
\newcommand\nlmath{$\hfill\mbox{}\\\mbox{}\hfill$}
\newcommand\nlnomath{\hfill\mbox{}\\\mbox{}\hfill}

%Dont include spaces for pretty print here
\newcommand\linemath[1]{\mbox{}\hfill$#1$\hfill\mbox{}\\}  
\newcommand\linemaths[2]{\mbox{}\hfill$#1$#2\hfill\mbox{}\\}  
\newcommand\linenomath[1]{\mbox{}\hfill{#1}\hfill\mbox{}\\}  
%Dont include spaces for pretty print here
\newcommand\LINEmath[1]{\mbox{}\hfill$#1$\hfill\mbox{}}
\newcommand\LINEmaths[2]{\mbox{}\hfill$#1$#2\hfill\mbox{}}
\newcommand\LINEnomath[1]{\mbox{}\hfill{#1}\hfill\mbox{}}
%Dont include spaces for pretty print here

\newcommand\mysection
[1]{\noindent{\Large\bf#1}\addcontentsline{toc}{section}{#1}}
\newcommand\mysubsection
[1]{\noindent{\Large\bf#1}\addcontentsline{toc}{subsection}{#1}}
\newcommand\mysubsubsection
[1]{\noindent{\bf#1}\addcontentsline{toc}{subsubsection}{#1}}

\newcommand\knuthquotation[2]
{{\footnotesize\begin{flushright}{\sl#1\par}{\noindent\sc--- #2}\end
{flushright}}}

% The fol. \par\noindent\initial{A} writes an initial letter A 
% Note that it was designed to have the bottom line exactly on
% the bottom line of the line it starts. So it works well with
%   \initial{\underline{\underline{\underline{\underline{First case:}}}}}
%   In the first case we have the following...
% The two texts "first case" share their bottom. The underline extends
% below it.
% If you do not want your intials to get the bottom line
% from the bottom line of the first but of the second line
% you must design another macro or use \initial{\raisebox{-3.5ex}{...}}

\newbox\yinibox
\def\initial#1{\par
\noindent
\setbox\yinibox\hbox{#1}%
\setbox\yinibox\vbox to \ht\yinibox{\offinterlineskip\hbox{{#1}~~}\vss}%
\leavevmode
\hangindent=\wd\yinibox
\hangafter=-2
\hbox to0pt{\hskip-\hangindent\box\yinibox\hfill}\ignorespaces}
   
%%% Parentheses: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\mathcommand\inparentheses[1]{\left(\begin{array}[c]{l}#1\end{array}\right)}
\mathcommand\inbrackets[1]{\left[\begin{array}[c]{l}#1\end{array}\right]}
\mathcommand\inbraces[1]{\left\{\begin{array}[c]{l}#1\end{array}\right\}}
\mathcommand\inparenthesestight
[1]{\left(\begin{array}{@{}l@{}}#1\end{array}\right)}
\mathcommand\inparenthesesinline[1]{(\ #1\ )}
\mathcommand\inpit[1]{(#1)}
\mathcommand\inbracesit[1]{\{#1\}}
\mathcommand\inparenthesesinlinetight[1]{\inpit{#1}}
\newcommand\mathinparenthesesinlinetight[1]{(#1)}%allows line breaking
\mathcommand\noparenthesesoplist[1]
{{\begin{array}{r l}\relax&#1\\\end{array}}}
\mathcommand\noparenthesesoplisttop[1]
{{\begin{array}[t]{r l}\relax&#1\\\end{array}}}
\mathcommand\inparenthesesoplist[1]
{{\left(\noparenthesesoplist{#1}\right)}}
\mathcommand\inbracesoplist[1]
{{\left\{\noparenthesesoplist{#1}\right\}}}
\mathcommand\inbracketsoplist[1]
{{\left[\noparenthesesoplist{#1}\right]}}
\newcommand\oplistund        {\\\tightund        &}
\newcommand\oplistoder       {\\\tightoder       &}
\newcommand\oplistcup        {\\\tightcup        &}
\newcommand\oplistuplus      {\\\tightuplus      &}
\newcommand\oplistequivalent {\\\tightequivalent &}
\newcommand\oplistimplies    {\\\tightimplies    &}
\newcommand\oplistcirc       {\\\tightcirc       &}
\newcommand\oplistantiimplies{\\\tightantiimplies&}
\newcommand\oplistnl         {\\                 &}
\mathcommand\inparenthesesimplies[2]{{\left(\begin{array}{l l}
\multicolumn{2}{l}{#1}\\\tightimplies&#2\\\end{array}\right)}}
\newcommand\inparenthesesimpliestoplevel[3]
{\math{#1\left(\begin{array}{l}\majorheadroom\footroom#2
 \\\end{array}\right.}\\\getittotheright{\math{
 \left.\begin{array}{l l}\tightimplies&\majorheadroom\footroom#3
 \\\end{array}\right)}}} 

\newcommand\opta{{\rm[}}
\newcommand\opte{{\rm]}}
\newcommand\opt[1]{\opta#1\/\opte}
\mathcommand\displayopt
[1]{\left[\begin{array}[t]{@{\,}c@{\,}}#1\end{array}\right]}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% MATH NOTATION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand\stopq{\math{.}\penalty-1\relax\,\,} %\penalty-10 is too low
\mathcommand\hastype[2]{{#1}:\,{#2}}
\mathcommand\tighthastype[2]{{#1}\tight:{#2}}
\mathcommand\prettytighthastype[2]{{#1}\,\tight:\:{#2}}
\mathcommand\typed[3]{#1\hastype{#2}{#3}\stopq}
\mathcommand\comma{,\ \ }
\mathcommand\setwithstart{\{\ }
\newcommand\setwithmark{~\math|\penalty-9\relax\,\ } 
%\penalty-10 is too low, \penalty-1 is too high
\mathcommand\setwithmarkq[1] {\ |_{#1}\ }
\mathcommand\setwithstop     {\ \}}
\newcommand\setwith
[2]{\math{\setwithstart#1}\setwithmark\math{#2\setwithstop}}
%should not be mathcommand for enabling \penalty-1
\mathcommand\displaysetwith
[2]{{\left\{\begin{array}{@{\ \ }l@{\ \ }|@{\ \ }l@{\ \ }}#1&#2\\\end
{array}\right\}}}
\mathcommand\displayset
[1]{{\left\{\begin{array}{@{\ \ }l@{\ \ }}#1\\\end{array}\right\}}}

\newcommand\tight[1]{\math{#1}}
\newcommand\tightsubseteq   {\tight\subseteq  }
\newcommand\tightnotsubseteq{\tight\nsubseteq }
\newcommand\tightsuperseteq {\tight\superseteq}
\newcommand\tightsetminus   {\tight\setminus  }
\newcommand\tightplus       {\tight+          }
\newcommand\tighttimes      {\tight\times     }
\newcommand\tightcap        {\tight\cap       }
\newcommand\tightcup        {\tight\cup       }
\newcommand\tightuplus      {\tight\uplus     }
\newcommand\tightcirc       {\tight\circ      }
\newcommand\tightin         {\tight{\,\in\,}  }
\newcommand\tightnotin      {\tight{\,\not\in\,}  }
\newcommand\tightni         {\tight{\,\ni\,}  }
\newcommand\tightnotni      {\tight{\,\not\ni\,}  }
\newcommand\tightequal      {\tight{\,=\,}\penalty-1\relax}
\newcommand\tightnotequal   {\tight{\,\not=\,}}
\newcommand\tightpreceq     {\tight{\,\preceq\,}}
\newcommand\tightprec       {\tight{\,\prec\,}}
\newcommand\tightnotprec    {\tight{\,\nprec\,}}
\newcommand\tightsucceq     {\tight{\,\succeq\,}}
\newcommand\tightsucc       {\tight{\,\succ\,}}
\newcommand\tightgtr        {\tight{\,>\,}}
\newcommand\tightless       {\tight{\,<\,}}
\newcommand\tightleq        {\tight{\,\leq\,}}
\newcommand\tightgeq        {\tight{\,\geq\,}}

\newcommand\boldequal  {\tight=}
\newcommand\boldunequal{\tight{\not=}}
\newcommand\boldless   {\tight<}
\newcommand\boldnotless{\tight{\not<}}
\newcommand\boldimplies{\tight\tightimplies}
\newcommand\Defnombox{{\rm Def}}
\newcommand\Def{\mbox{\Defnombox}}
\mathcommand\DEF{\Defnombox\:}

%\mathcommand\tightimplies{\rightarrow}    
%\mathcommand\tightantiimplies{\leftarrow}
%\mathcommand\tightequivalent{\leftrightarrow}
\mathcommand\tightimplies{\Rightarrow}
\mathcommand\tightantiimplies{\Leftarrow}
\mathcommand\tightequivalent {\Leftrightarrow}
% The one-line arrow for implication is preferable for the following reasons:
% (1) Hilbert & Bernays uses this symbol.
% (2) In intuitionistic logic, (A->B) can be seen as
%     The type of functions that transform a proof of A
%     to a proof of B, and the implication is valid,
%     if such a function exists.
% The two-line arrow is preferable for the following reason:
% (A) It is more readable in formulas with type declarations and 
%     with \mapsto as a symbol for substitution. Note that the replacement
%     of "x\mapsto y" with "y/x" has two problems again:
%     (a) This would cost me a week to replace it in all contexts.
%     (b) Readability is destroyed by the replacement, because some idiots
%         use "x/y" instead of "y/x".   
% (B) The equivalence looks more like "=" which it actually is.
\mathcommand\tightund        {\wedge}
\mathcommand\tightoder       {\vee}
\mathcommand\tightshefferstroke
% {|}
%Peckhaus: Sheffer stroke sollte größer und fetter sein, etwa mit dem TeX-Befehl \mid (oder verwenden sie ihn schon?).
{\mid}
\mathcommand\tightuparrow{\uparrow}
\def       \implies      {\ \tightimplies      \penalty-2\relax\ }
\newcommand\und          {\ \tightund          \penalty-2\relax\ }
\newcommand\oder         {\ \tightoder         \penalty-2\relax\ }
\newcommand\antiimplies  {\ \tightantiimplies  \penalty-2\relax\ }
\newcommand\equivalent   {\ \tightequivalent   \penalty-2\relax\ }
\newcommand\shefferstroke{\ \tightshefferstroke\penalty-2\relax\ }

\newcommand \id          {{\rm id}}
\mathcommand\allall      {\mathcal{V}}
\mathcommand\allsets     {\POWER\allall}
\mathcommand\allfinitesets{\FINITE\allall}
\mathcommand\urelements  {\mathcal{U}}
\mathcommand\algebra     {\mathcal{A}}
\mathcommand\balgebra    {\mathcal{B}}
\mathcommand\calgebra    {\mathcal{C}}
\mathcommand\dalgebra    {\mathcal{D}}
\mathcommand\ialgebra    {\mathcal{I}}
\mathcommand\salgebra    {\mathcal{S}}
\mathcommand\walgebra    {\mathcal{W}}
\mathcommand\ralgebra    {\mathcal{R}}
\mathcommand\algebraprime{\mathcal{A}'}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mathapplycommand\FLD        {\rm field}
\mathapplycommand\DOM        {\rm dom}
\mathapplycommand\RAN        {\rm ran}
\mathapplycommand\kernel     {\rm ker}
% \mathapplycommand\FINITE     {\mbox{\fraknomath P}_\N}%for \frak from german
% \mathapplycommand\POWER      {\mbox{\fraknomath P}}
% \mathapplycommand\posfinPOWER{\mbox{\fraknomath P}_\posN\!}
\mathapplycommand\FINITE     {{\mathfrak P}_{\scriptscriptstyle\N}}%for \frak from amssymb
\mathcommand\POWERSYM        {{\mathfrak P}}
\mathapplycommand\POWER      {\POWERSYM}
\mathapplycommand\posfinPOWER{\POWERSYM_{\scriptscriptstyle\posN\!}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mathcommand\CARD[1]         {\,|{#1}|\,}
\mathcommand\FLOOR[1]        {\ \lfloor#1\rfloor\ }
\mathcommand\CEIL[1]         {\ \lceil#1\rceil\ }
\mathcommand\reverserelation[1]{{#1}^{-1}}
%\mathcommand\restrictedto[1]{|_{#1}}
\mathcommand\domres[2]{{_{#2}\tight\upharpoonleft#1}}
\mathcommand\ranres[2]{{#1\tight\upharpoonright_{#2}}}
\mathcommand\funarg[1]{(#1)}
\mathcommand\app[2]{#1(#2)}
\mathcommand\displayapp[2]{#1\inparentheses{#2}}
\mathcommand\displayapptight[2]{#1\inparenthesestight{#2}}
\mathcommand\apptotuple[2]{#1#2}
\mathcommand\relapp[2]{\langle#2\rangle#1}
\mathcommand\displayrelapp
[2]{\left\langle\begin{array}{@{}l@{}}#2\end{array}\right\rangle\!#1}
\mathcommand\relappsin[2]{\relapp{#1}{\!\{#2\}\!}}
\mathcommand\revrelapp[2]{#1\langle#2\rangle}
\mathcommand\displayrevrelapp
[2]{#1\!\left\langle\begin{array}{@{}l@{}}#2\end{array}\right\rangle}
\mathcommand\revrelappsin[2]{\revrelapp{#1}{\!\{#2\}\!}}
\mathcommand\displayrevrelappsin[2]{\displayrevrelapp{#1}{\!\left\{#2\right\}\!}}
\mathcommand\pair[2]{(#1,#2)}
\mathcommand\displaypair[2]{\inparentheses{#1,\ \ #2}}
\mathcommand\trip[3]{(#1,#2,#3)}
\mathcommand\displaytrip[3]{\inparentheses{#1,\ \ #2,\ \ #3}}
\mathcommand\superdisplaytrip[3]{\left(\begin
{array}{l}#1,\\#2,\\#3,\\\end{array}\right)}
\mathcommand\quar[4]{(#1,#2,#3,#4)}
\mathcommand\displayquar[4]{\inparentheses{#1,\ \ #2,\ \ #3,\ \ #4}}
\mathcommand\superdisplayquar[4]{\left(\begin
{array}{l}#1,\\#2,\\#3,\\#4\\\end{array}\right)}
\mathcommand\quin[5]{(#1,#2,#3,#4,#5)}
\mathcommand\displayquin[5]{\inparentheses{#1,\ \ #2,\ \ #3,\ \ #4,\ \ #5}}
\mathcommand\sext[6]{(#1,#2,#3,#4,#5,#6)}
\mathcommand\sept[7]{(#1,#2,#3,#4,#5,#6,#7)}
\mathcommand\oct[8]{(#1,#2,#3,#4,#5,#6,#7,#8)}
\mathcommand\ninetuple[9]{(#1,#2,#3,#4,#5,#6,#7,#8,#9)}
\newcommand\tentuple[9]{(#1,#2,#3,#4,#5,#6,#7,#8,#9,\singletonrest}
\newcommand\singletonrest[1]{#1)}
\newcommand\elev[9]{(#1,#2,#3,#4,#5,#6,#7,#8,#9,\pairrest}
\newcommand\pairrest[2]{#1,#2)}
\mathcommand\setwithq[3]     {\setwithstart#2\setwithmarkq{#1}#3\setwithstop}
\mathcommand\setofwords[1]{#1^{\textstyle\ast}}
\mathcommand\setofwordsscriptstyle[1]{#1^{\ast}}
\mathcommand\setofnonemptywords[1]{#1^+}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mathcommand\FUNSET   [2]{{#1}\rightarrow{#2}}
\mathcommand\PARFUNSET[2]{{#1}\leadsto   {#2}}
\mathcommand\FUNDEF   [3]{\hastype{#1}{\FUNSET   {#2}{#3}}}
\mathcommand\PARFUNDEF[3]{\hastype{#1}{\PARFUNSET{#2}{#3}}}
%categories
\mathcommand\morphcolon{::}
\mathcommand\morpharrow{\rightarrow}
\mathcommand\morph  [3]{{#1}\morphcolon{#2}\morpharrow{#3}}
\newcommand\Idname{{\rm Id}}
\mathcommand\Id[1]{{\Idname_{#1}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mathcommand\equiclass[2]{{#1}{[\{{#2}\}]}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mathcommand\aritysugarsymbol{\rightarrow}
\mathcommand\aritysugar{\ \aritysugarsymbol\ }

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mathcommand\monus{\mathchoice
{\raisebox{-.4ex}{$\dot{\raisebox{.4ex}[0ex]{$-$}}$}}%     display-style
{\raisebox{-.4ex}{$\dot{\raisebox{.4ex}[0ex]{$-$}}$}}%     text-style
{\raisebox{-.3ex}{$\scriptstyle\dot{\raisebox{.3ex}[0ex]
{$\scriptstyle-$}}$}}                                %     scriptstyle
{\raisebox{-.2ex}{$\scriptscriptstyle\dot{\raisebox{.2ex}[0ex]
{$\scriptscriptstyle-$}}$}}                          %scriptscriptstyle
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\mathcommand\yields{\;\vdash\;}
\mathcommand\antiyields{\;\dashv\;}
\mathcommand\tightyields{\vdash}
\mathcommand\tightantiyields{\dashv}
\mathcommand\notyields{\;\nvdash\;}
\mathcommand\refltransyields{\hspace{0.5em}\raisebox{1.3ex}{\math{\scriptstyle
  \ast}}\hspace{-1.0em}\yields}
\mathcommand\transyields
{\hspace{0.5em}\raisebox{1.3ex}{$\scriptscriptstyle%\oplus
+$}\hspace
{-1.0em}\yields\hspace{0.3em}}
\mathcommand\notmodels{\:\not\!\models}

\newcommand\EVALSYM{{\rm eval}}
\mathapplycommand\EVAL{\EVALSYM}
\mathcommand\V{{\rm V}}
\mathcommand\X{{\rm X}}
\newcommand\nottight{\bigmath}
\mathcommand\refltransclosureinline[1]{{#1}^\ast}
\mathcommand\VARSYM {\mathcal{V}}
\mathapplycommand\VAR{\VARSYM}
\mathcommand\VARnoparentheses[1]{\VARSYM #1}
\mathcommand\VARsingleindex[1]{\VARSYM\!_{{#1}}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ZAHLENMENGEN %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \N        Set of natural numbers
% \posN     Set of positive natural numbers
% \ordclass Proper class of ordinal numbers
% \ZZ       Set of integers
% \Q        Set of rationals
% \RE       Set of real numbers
% \posRE    Set of positive real numbers
% \nonnegRE Set of non-negative real numbers
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% \mathcommand\N{{\rm
% %\rm must be out here because on rare occursions does not work
% %infront of the I\hskip....
% %\ifmmode%  Sind wir im Mathemodus ?
% \mathchoice{{I\hskip -2pt   N}}% display-style
%            {{I\hskip -2pt   N}}% text-style
%            {{I\hskip -1.5pt N}}% scriptstyle
%            {{I\hskip -1pt   N}}% scriptscriptstyle
% %\else\math{\rm I\hskip-2pt N}\fi
% }}
% \newcommand\ZZ{{\rm\ifmmode\mathchoice{{Z\hskip -4pt Z}}{{Z\hskip -4pt Z}}
% {{Z\hskip -3pt Z}}{{Z\hskip -3pt Z}}\else\mbox{\tenrm Z\hskip-4pt Z}\fi}}
\mathcommand\N{{\bf N}}
\mathcommand\posN{\N_{\:\!\!\mbox{\sixsf+}}}
\mathcommand\ZZ{{\bf Z}}
\mathcommand\Q{{\bf Q}}
\mathcommand\ordclass{\mathcal{O}}
%\newcommand\RE{{\rm\ifmmode\mathchoice{{I\hskip -2pt R}}{{I\hskip -2pt R}}
%{{I\hskip -1.5pt R}}{{I\hskip -1pt R}}\else{\tenrm I\hskip-2pt R}\fi}}
\mathcommand\RE{{\bf R}}
\mathcommand\posRE{\RE_{\scriptscriptstyle +}}
\mathcommand\nonnegRE{\RE_{\scriptscriptstyle\succeq0}}

\mathcommand\Qzero{{\cal Q}_0}
\newcommand\squaredot{\,\rule{0.4ex}{0.4ex}\,}

%Transitive closures
\mathcommand\transclosure[1]{\stackrel{\scriptscriptstyle+}{#1}}
\mathcommand\transclosureinline[1]{{#1}^{\scriptscriptstyle+}}

%_____________________________________________________________________________
%Signatures
\mathcommand\sigarity{\alpha}
\newcommand\sig{{\rm sig}}
\mathcommand\sigsorts  {{\mathbb S}}
\mathcommand\sigfunsym {{\mathbb F}}
\mathcommand\consfunsym{{\mathbb C}\,} 
% \, cures strange dvips bugg
\mathcommand\deffunsym {{\mathbb N}}
\mathcommand\Ax{\mathcal{AX}}

%from header.tex
%_____________________________________________________________________________
%Reduction relation

%\red...
%\notred
%\redpara
%\revpara
%\simpara
%\unired
\mathcommand\unired{\Longrightarrow}
\mathcommand\redsimple{\longrightarrow}
\mathcommand\redindex[1]{\redsimple_{_{\!#1}}}
\mathcommand\notredindex[1]{\,\,\,\not\!\!\!\!\redsimple_{_{\!#1}}}
\newcommand\redsub             {\redindex{\R ,\X        }}
\newcommand\redsubprime        {\redindex{\R',\X'       }}
\newcommand\redshortsub        {\redindex{\R ,\V        }}
\newcommand\redshortsubprime   {\redindex{\R',\V'       }}
\newcommand\redsubY            {\redindex{\R ,\Y        }}
\newcommand\redsubemptyset     {\redindex{\R ,\emptyset }}
\newcommand\redsubprimeemptyset{\redindex{\R',\emptyset }}
\newcommand\redsubVsig         {\smallfootroom\redindex{\R ,\Vsig     }}
\newcommand\redsubVsigprime    {\smallfootroom\redindex{\R',\Vsigprime}}
\mathcommand\redindexn[2]{\stackrel{#1}\redsimple_{_{\!#2}}}
\mathcommand\redparaindex[1]{\redpara_{\hskip-1.5pt\scriptscriptstyle#1}}
\mathcommand\revparaindex[1]{\revpara_{\hskip-1.5pt\scriptscriptstyle#1}}
\mathcommand\simparaindex[1]{\simpara_{\hskip-1.5pt\scriptscriptstyle#1}}
\mathcommand\uniredindex[1]{\unired_{\hskip-1.5pt\scriptscriptstyle#1}}

%\antired...
%\notantired..
%\antiredpara...
%\antirevpara...
%\antiunired...
\mathcommand\antiunired{\Longleftarrow}
\mathcommand\antired{\longleftarrow}
\mathcommand\antiuniredindex[1]{\antiunired_{_{\!#1}}}
\mathcommand\antiredindex[1]{\antired_{_{\!#1}}}
\mathcommand\notantiredindex[1]{\,\,\,\not\!\!\!\!\antired_{_{\!#1}}}
\newcommand\antiredsub          {\antiredindex{\R ,\X }}
\newcommand\antiredshortsub     {\antiredindex{\R ,\V }}
\newcommand\antiredshortsubprime{\antiredindex{\R',\V'}}
\newcommand\antiredsubVsig      {\smallfootroom\antiredindex{\R',\Vsig}}
\mathcommand\antiredindexn[2]{\stackrel{#1}\antired_{_{\!#2}}}
\mathcommand\antiredparaindex
[1]{\antiredpara_{\hskip-1.25pt\scriptscriptstyle#1}}
\mathcommand\antirevparaindex[1]
{\antirevpara_{\hskip-1.25pt\scriptscriptstyle#1}}

%\sym...
\mathcommand\sym{\longleftrightarrow}
\mathcommand\symindex[1]{\sym_{_{\!#1}}}
\mathcommand\symindexn[2]{\stackrel{#1}{\sym_{_{\!#2}}}}
\newcommand\symsub     {\symindex{\R,\X}}
\newcommand\symshortsub{\symindex{\R,\V}}
\newcommand\symsubVsig {\smallfootroom\symindex{\R,\Vsig}}

%Reflexive transitive closures
%Congruences
%\congru...
%\footnotecongru...
%\notcongru...
\mathcommand\refltransclosure[1]{\stackrel{\scriptstyle\ast}{#1}}
%{\mathop{#1}^{\scriptstyle\ast}}
\mathcommand\congru{\refltransclosure\sym}
\mathcommand\congruindex[1]{\congru_{_{\!#1}}}
\newcommand\congrusub             {\congruindex{\R ,\X            }}
\newcommand\congrushortsub        {\congruindex{\R ,\V            }}
\newcommand\congrusubVsig         {\smallfootroom\congruindex{\R ,\Vsig     }}
\newcommand\congrusubVsigprime    {\smallfootroom\congruindex{\R',\Vsigprime}}
\newcommand\congrusubemptyset     {\congruindex{\R ,\emptyset     }}
\newcommand\congrusubprimeemptyset{\congruindex{\R',\emptyset     }}
\mathcommand\footnotecongru%{\stackrel\footnoteoast\sym}
{\congru}
\mathcommand\footnotecongruindex[1]{\footnotecongru_{_{#1}}}
\mathcommand\notcongru{\hspace{0.6em}\not\hspace{-0.85em}\refltransclosure\sym}
\mathcommand\notcongruindex[1]{\notcongru_{_{\!#1}}}
\newcommand\notcongrusub        {\notcongruindex{\R,\X       }}
\newcommand\notcongrusubemptyset{\notcongruindex{\R,\emptyset}}

%Transitive closures
%\trans...
%\antitrans...
\mathcommand\trans{\transclosure\redsimple}
\mathcommand\transindex[1]{\trans_{_{\!#1}}}
\newcommand \transsub        {\transindex{\R,\X}}
\newcommand \transshortsub   {\transindex{\R,\V}}
\newcommand \transsubVsig    {\smallfootroom\transindex{\R,\Vsig}}
\newcommand \transsubemptyset{\transindex{\R,\emptyset}}
\mathcommand\antitrans{\transclosure\antired}
\mathcommand\antitransindex[1]{\antitrans_{_{\!#1}}}
\newcommand \antitranssub     {\antitransindex{\R,\X}}
\newcommand \antitransshortsub{\antitransindex{\R,\V}}
\newcommand \antitranssubVsig {\smallfootroom\antitransindex{\R,\Vsig}}

%Reflexive and transitive closures
%\refltrans...
%\footnoterefltrans...
%\notrefltrans...
%\antirefltrans...
%\footnoteantirefltrans...
\mathcommand\refltrans{\refltransclosure\redsimple}
\mathcommand\refltransindex[1]{\refltrans_{_{\!#1}}}
\newcommand \refltranssub          {\refltransindex{\R ,\X }}
\newcommand \refltranssubemptyset  {\refltransindex{\R ,\emptyset}}
\newcommand \refltranssubprime     {\refltransindex{\R',\X'}}
\newcommand \refltransshortsub     {\refltransindex{\R ,\V }}
\newcommand \refltransshortsubprime{\refltransindex{\R',\V'}}
\newcommand \refltranssubVsig      {\smallfootroom\refltransindex{\R ,\Vsig}}
\mathcommand\footnoterefltrans%{\stackrel\footnoteoast\redsimple}
{\refltrans}
\mathcommand\footnoterefltransindex[1]{\footnoterefltrans_{_{#1}}}
\newcommand \footnoterefltranssub     {\footnoterefltransindex{\R,\X}}
\newcommand \footnoterefltransshortsub{\footnoterefltransindex{\R,\V}}
\mathcommand\notrefltrans
            {\hspace{0.6em}\not\hspace{-0.85em}\refltransclosure\redsimple}
\mathcommand\antirefltrans{\refltransclosure\antired}
\mathcommand\antirefltransindex[1]{\antirefltrans_{_{\!#1}}}
\newcommand \antirefltranssub          {\antirefltransindex{\R ,\X }}
\newcommand \antirefltransshortsub     {\antirefltransindex{\R ,\V }} 
\newcommand \antirefltransshortsubprime{\antirefltransindex{\R',\V'}} 
\newcommand \antirefltranssubVsig      {\antirefltransindex{\R',\V'}} 
\mathcommand\footnoteantirefltrans%{\stackrel\footnoteoast\antired}
{\antirefltrans}
\mathcommand\footnoteantirefltransindex[1]{\footnoteantirefltrans_{_{#1}}}
\newcommand \footnoteantirefltranssub     {\footnoteantirefltransindex{\R,\X}}
\newcommand \footnoteantirefltransshortsub{\footnoteantirefltransindex{\R,\V}}

%joinability
\mathcommand\downarrowindex[1]{\downarrow_{_{#1}}}
\newcommand \downarrowsub        {\downarrowindex{\R ,\X       }}
\newcommand \downarrowsubemptyset{\downarrowindex{\R ,\emptyset}}
\newcommand \downarrowsubVsig    {\smallfootroom\downarrowindex{\R,\Vsig}}
\newcommand \downarrowsubprimeemptyset{\downarrowindex{\R',\emptyset}}
\mathcommand\notconfluindex[1]{\notconflu_{_{#1}}}
\newcommand \notconflusub        {\notconfluindex{\R,\X       }}
\newcommand \notconflusubemptyset{\notconfluindex{\R,\emptyset}}
\mathcommand\footnotenotconfluindex[1]{\footnotenotconflu_{_{#1}}}
\newcommand \footnotenotconflusub{\footnotenotconfluindex{\R,\X}}

%strong joinability
\mathcommand\downdownarrow        {\downdownarrows}
\mathcommand\downdownarrowindex[1]{\downdownarrow_{_{#1}}}
\newcommand \downdownarrowsub     {\downdownarrowindex{\R ,\X       }}

\mathcommand\reflclosure[1]{\stackrel
%{\raisebox{0.1em}{$\scriptscriptstyle\preceq$}{ 1}}
{\scriptscriptstyle=}
{#1}}
\mathcommand\reflclosureinline[1]{{#1}^{\scriptscriptstyle=}}
\mathcommand\onlyonce
%{{\displaystyle\mathop{\redsimple}^{{\leq}1}}}
{\reflclosure\redsimple}
\mathcommand\antionlyonce{\reflclosure\antired}
\mathcommand\onlyonceindex[1]{\onlyonce_{_{\!#1}}}
\mathcommand\antionlyonceindex[1]{\antionlyonce_{_{\!#1}}}

\mathapplycommand\nf{\rm NF}

\mathcommand\toconditiontermssub     {\twoheadrightarrow_{_{\R,\X}}}
\mathcommand\toconditiontermssubY    {\twoheadrightarrow_{_{\R,\Y}}}
\mathcommand\toconditiontermsshortsub{\twoheadrightarrow_{_{\R,\V}}}

%_____________________________________________________________________________
%Variables notation
\newcommand \U{{\rm U}}
\newcommand \Y{{\rm Y}}
\newcommand \Z{{\rm Z}}
\mathcommand\Xprime{{\rm X}'}
\mathcommand\Yprime{{\rm Y}'}
\mathcommand\Xprimeprime{{\rm X}''}
\newcommand \SIG     {{\rm SIG}}
\mathcommand\CONS    {\mathcal{C}}
\mathcommand\SIGsort     [1]{(\SIG     ,#1)}
\mathcommand\CONSsort    [1]{(\CONS    ,#1)}
\mathcommand\varsigmasort[1]{(\varsigma,#1)}
\mathcommand\SIGsortindex     [1]{_{\SIG ,#1}}
\mathcommand\CONSsortindex    [1]{_{\CONS,#1}}
\mathcommand\DUNNOsortindex   [1]{_{\DUNNO,#1}}
\mathcommand\varsigmasortindex[1]{_{\varsigma,#1}}
\mathcommand\Vsig      {\V \!_{\SIG }}
\mathcommand\Xsig      {\X   _{\SIG }}
\mathcommand\Vcons     {\V \!_{\CONS}}
\mathcommand\Sigmacons {\Sigmaoffont_{\CONS}}
\mathcommand\Xcons     {\X   _{\CONS}}
\mathcommand\Vconsprime{\V'\!_{\CONS}}
\mathcommand\Vsigprime {\V'\!_{\SIG }}
\mathcommand\sigV      {\Vsig\!\uplus\!\Vcons}
\mathcommand\sigVprime {\Vsigprime\!\uplus\!\Vconsprime}
\mathcommand\hiddenVindi     [2]{\V   \!_{{#1},{#2}}}
\mathcommand\hiddenXindi     [2]{\X     _{{#1},{#2}}}
\mathcommand\hiddenVprimeindi[2]{\V'\!\!_{{#1},{#2}}}
\newcommand \Vsigindex     [1]{\hiddenVindi\SIG     {#1}}
\newcommand \Xsigindex     [1]{\hiddenXindi\SIG     {#1}}
\newcommand \Vconsindex    [1]{\hiddenVindi\CONS    {#1}}
\newcommand \Xconsindex    [1]{\hiddenXindi\CONS    {#1}}
\newcommand \Vvarsigmaindex[1]{\hiddenVindi\varsigma{#1}}
\newcommand \Xvarsigmaindex[1]{\hiddenXindi\varsigma{#1}}
\mathapplycommand\VARCONS{\VARsingleindex\CONS}
\mathapplycommand\VARSIG {\VARsingleindex\SIG}
\mathapplycommand\VARord {\VARsingleindex\boldless}

%_____________________________________________________________________________
%Term notation
\mathcommand\vt{\mathcal{ T}}
\mathcommand\gt{\mathcal{GT}}
\mathcommand\hiddenvtindi[2]{\mathcal{ T}\!_{#1,#2}}
\mathcommand\hiddengtindi[2]{\mathcal{GT}\!_{#1,#2}}
\newcommand\vtsigindex     [1]{\hiddenvtindi{\SIG     }{#1}}
\newcommand\vtconsindex    [1]{\hiddenvtindi{\CONS    }{#1}}
\newcommand\vtvarsigmaindex[1]{\hiddenvtindi{\varsigma}{#1}}
\newcommand\gtsigindex     [1]{\hiddengtindi{\SIG     }{#1}}
\newcommand\gtconsindex    [1]{\hiddengtindi{\CONS    }{#1}}
\newcommand\gtvarsigmaindex[1]{\hiddengtindi{\varsigma}{#1}}
\mathapplycommand\hiddentv     {\mathcal{T}}
\mathapplycommand\hiddentg     {\mathcal{GT}}
\mathapplycommand\hiddentvprime{\mathcal{T}'}
%ground term sets
\newcommand\tgcons              {\hiddentg\cons }
\newcommand\tgsig               {\hiddentg\sig  }   
\newcommand\tgdunno             {\hiddentg\dunno}
\newcommand\tgconsprime         {\hiddentg{\cons'}}
\newcommand\tgsigprime          {\hiddentg{\sig' }}
\newcommand\tgunderlinecons     {\hiddentg{\underline{\underline{\cons }}}}
\newcommand\tgunderlineconsprime{\hiddentg{\underline{\underline{\cons'}}}}
%non-ground term sets
% variables from \Vsig or \Vsigprime
\newcommand\tsigV        {\hiddentv{\sig  ,\V}}
\newcommand\tsigVsig     {\hiddentv{\sig  ,\Vsig}}
\newcommand\tsigVsigprime{\hiddentv{\sig' ,\Vsigprime}}
% variables from \Vcons 
\newcommand\tcc{\hiddentv{\cons,\Vcons}}
% variables from \Vcons\cup\Vsig etc.
\newcommand\tss          {\hiddentv{\sig  ,\sigV     }}
\newcommand\tcs          {\hiddentv{\cons ,\sigV     }}
\newcommand\tcsprime     {\hiddentv{\cons',\sigVprime}}
% variables from \X or \X' etc.
\newcommand\tsigX        {\hiddentv{\sig ,\X }}
\newcommand\tconsX       {\hiddentv{\cons,\X }}
\newcommand\tsigXprime   {\hiddentv{\sig',\X'}}
\newcommand\tconsXprime  {\hiddentv{\cons',\X'}}
\newcommand\tconsVconsX  {\hiddentv{\cons,\Xcons}}
% variables from \Y
\newcommand\tsigY        {\hiddentv{\sig ,\Y }}
\newcommand\tconsY       {\hiddentv{\cons,\Y }}
%term algebras
\newcommand\tconsXalt {\app{{\mathcal T}_\CONS}\X}
\newcommand\tconsValt {\app{{\mathcal T}_\CONS}\V}
\newcommand\tX        {\hiddentv\X}
\newcommand\tXprime   {\hiddentv{\X'}}
\newcommand\tV        {\hiddentv\V}
\newcommand\tY        {\hiddentv\Y}
\newcommand\temptyset {\hiddentv\emptyset}
\newcommand\tVsig     {\hiddentv\Vsig}
\newcommand\tVsigprime{\hiddentvprime\Vsigprime}
% \newcommand{\gtc}{\hiddentg{\cons}}
%_____________________________________________________________________________
%substitutions
\mathcommand\SUBSYM{\mathcal{SU\hspace{-.08em}B}}
\mathdoubleapplycommand\SUBST{\SUBSYM}
\newcommand \Xsubst     {\SUBST\V\tX   }
\newcommand \Vsubst     {\SUBST\V\vt   }
\newcommand \Vsigsubst  {\SUBST\V\tVsig}
\newcommand \Gsubst     {\SUBST\V\gt   }
\mathcommand\Isubst     {{\rm CGSUB}(\V ,\cons )}
\mathcommand\Isubstprime{{\rm CGSUB}(\V',\cons')}
\mathcommand\GENSYM     {\mathcal{G\hspace{-.04em}E\hspace{-.09em}N}}
\mathcommand\GSSYM      {{\GENSYM\hspace{-.14em}}\SUBSYM}
\mathdoubleapplycommand\GS{\GSSYM}
\newcommand\VGS{\GS\V\vt}
\newcommand\XGS{\GS\V\tX}
\newcommand\VsigGS{\GS\V\tVsig}
%
\mathcommand\POSSYMBOL{\mathcal{P\hspace{-.08em}O\hspace{-.1em}S}}
\mathcommand\VPOSSYMBOL{\V\hspace{-.04em}\POSSYMBOL}
\mathcommand\FPOSSYMBOL{\sigfunsym\hspace{-.04em}\POSSYMBOL}
\mathapplycommand\TPOS{\POSSYMBOL}
%\mathapplycommand\POS{\POSSYMBOL} \POS is also used by xy. Use \TPOS instead!
\mathapplycommand\VPOS{\VPOSSYMBOL}
\mathapplycommand\FPOS{\FPOSSYMBOL}
%\mathcommand\OCCSYMBOL{\mathcal{O}}
%\mathapplycommand\OCC{\OCCSYMBOL}%obsolete but still in use
\mathcommand\neitherprefixsymbol{\parallel}
\mathcommand\neitherprefix[2]{{#1}\,\neitherprefixsymbol\,{#2}}
\mathcommand\replsuffix   [2]{[\,#1\leftarrow#2\,]}      %use \repl if possible
\mathcommand\replparsuffix[3]{\replsuffix{#1}{#2\ |\ #3}}%use \replpar
\mathcommand\repl         [3]{#1\penalty-1\replsuffix{#2}{#3}}
\mathcommand\replpar      [4]{#1\penalty-1\replparsuffix{#2}{#3}{#4}}
\mathcommand\eqvariablessig[1]{\mbox{\rm Eq}(\sig,{#1})}
\newcommand\eqvsig{\eqvariablessig{\sigV}}
\mathcommand\eqgsig{\mbox{\rm GEq}(\sig)}
\mathcommand\direqv[1]{\mbox{\rm DEq}(#1)}
\newcommand\direqvariablessig[1]{\direqv{\sig,{#1}}}
\newcommand\direqvsig{\direqv{\sig,\sigV}}
\mathapplycommand\MGU{\rm Mgu}
\mathdoubleapplycommand\minmgu{\rm mgu}
\mathdoubleapplycommand\sep{\rm Sep}
\mathdoubleapplycommand\minsep{\rm sep}
\mathapplycommand\depth{\rm depth}
\mathapplycommand\size{\rm size}
\newcommand\monotonic           {\tsigX-mono\-tonic}
\newcommand\Vmonotonic          {\vt-mono\-tonic}
%\newcommand\amonotonic          {an \X-mono\-tonic}
\newcommand\emptysetmonotonic   {\gt-mono\-tonic}
\newcommand\monotonicity        {\tsigX-mono\-toni\-city}
\newcommand\Vmonotonicity       {\vt-mono\-toni\-city}
%\newcommand\Monotonicity        {\X-mono\-toni\-city}
\newcommand\stable              {\X-stable}
\newcommand\Vstable             {\V-stable}
\newcommand\Ystable             {\Y-stable}
\newcommand\emptysetstable      {\mbox{$\emptyset$}-stable}
\newcommand\stability           {\X-stabi\-lity}
\newcommand\Stability           {\X-stabi\-lity}
\newcommand\Vstability          {\V-stabi\-lity}
\newcommand\VStability          {\V-stabi\-lity}
\newcommand\compatible          {\X-compa\-tible}
\newcommand\RXcompatible        {\RX-compa\-tible}
\newcommand\Vcompatible         {\V-compa\-tible}
\newcommand\Ycompatible         {\Y-compa\-tible}
\newcommand\leftrightcompatible {\X-left-right-compa\-tible}
\newcommand\Vleftrightcompatible{\V-left-right-compa\-tible}
\newcommand\dontcarecompatible  {\X-don't-care-compa\-tible}
\newcommand\aleftrightcompatible{an \X-left-right-compa\-tible}
\newcommand\adontcarecompatible {an \X-don't-care-compa\-tible}
\newcommand\compatibility       {\X-compa\-ti\-bility}
\newcommand\dontcarecompatibility{\X-don't-care-compa\-ti\-bility}
\newcommand\Vdontcarecompatible {\V-don't-care-compa\-tible}
\newcommand\Safety              {Safeness}
\newcommand\safety              {safeness}
\newcommand\safe                {safe}
\newcommand\Safe                {Safe}
\newcommand\unsafe              {unsafe}
\newcommand\safely              {safely}
\newcommand\constructorminimal{con\-struc\-tor-mini\-mal}
\newcommand\ConstructorMinimal{Con\-struc\-tor-Mini\-mal}
\newcommand\constructorminimality{con\-struc\-tor-mini\-mal\-ity}
\newcommand\constructorminimum{con\-struc\-tor-mini\-mum}
\newcommand\constructorpreserving{con\-struc\-tor-pre\-serving}
\newcommand\constructorpreservation{con\-struc\-tor-pre\-serva\-tion}
\newcommand\constructorbased{con\-struc\-tor-based}
\newcommand\Constructorbased{Con\-struc\-tor-based}
\newcommand\terminationpair{termi\-na\-tion-pair}
\newcommand\TerminationPair{Termi\-na\-tion-Pair}
\newcommand\inductivesubstitution{constructor ground substitution}
\newcommand\aninductivesubstitution{a constructor ground substitution}
\newcommand\Inductivesubstitution{Constructor ground substitution}
\newcommand\InductiveSubstitution{Constructor Ground Substitution}
\newcommand\inductiveinstance{constructor ground instance}

%Subterm
\newcommand\hiddensubST{_{_{\rm ST}}}
\mathcommand\superterm   {\rhd\hiddensubST}
\mathcommand\notsuperterm{\ntriangleright\hiddensubST}
\mathcommand\subterm     {\lhd\hiddensubST}
\mathcommand\notsubterm  {\ntriangleleft\hiddensubST}
\mathcommand\supertermeq {\trianglerighteq\hiddensubST}
\mathcommand\subtermeq   {\trianglelefteq\hiddensubST}

\mathcommand\sugarregel{l\boldequal r\rulesugar C}
\mathcommand\sugarregelindex[1]{l_{#1}\boldequal r_{#1}\rulesugar C_{#1}}
\mathcommand\sugaruncondregelindex[1]{l_{#1}\boldequal r_{#1}}
\mathcommand\ndrulewithassumption[3]{{{{\scriptstyle\lbrack}#1{\scriptstyle
\rbrack}}\atop\scriptstyle #2}\over #3}

%_____________________________________________________________________________
%Rules
\def\R{{\rm R}}
\mathcommand\RCONS{\R_\CONS}
\mathcommand\Rprime{{\rm R}'}
\mathcommand\RX{\R,\X}
\mathcommand\RCONSX{\RCONS,\X}
\mathcommand\DEFUNSYM{\mathcal{DEFUN}}
\mathapplycommand\DEFUN{\DEFUNSYM}
\newcommand\defsort{{\rm def}}
\mathcommand\ATSYM  {\mathcal{A\hspace{-.02em}T}}
\mathdoubleapplycommand\atomsof{\ATSYM}
\newcommand\atoms      {\atomsof\sig\V}
\newcommand\Xatoms     {\atomsof\sig\X}
\newcommand\Yatoms     {\atomsof\sig\Y}
\newcommand\scatoms    {\atomsof\sig\Vcons}
\mathcommand\GENATSYM  {\GENSYM\hspace{-.18em}\ATSYM}
\mathdoubleapplycommand\genatomsof{\GENATSYM}
\newcommand\genatoms      {\genatomsof\sig\V}
\newcommand\Xgenatoms     {\genatomsof\sig\X}
\newcommand\Ygenatoms     {\genatomsof\sig\Y}
\mathcommand\CONDSYM  {\mathcal{C\hspace{-.1em}O\hspace{-.12em}N\hspace{-.12em}D}}
\mathcommand\LITSYM   {\mathcal{LI\hspace{-.04em}T}}
\mathcommand\CONDLITSYM{\CONDSYM\hspace{-.04em}\LITSYM}
\mathapplycommand\condlitwitharg{\CONDLITSYM}
\newcommand\condlit {\condlitwitharg{\sig,\V}}
\newcommand\Xcondlit{\condlitwitharg{\sig,\X}}
\newcommand\Ycondlit{\condlitwitharg{\sig,\Y}}
\mathdoubleapplycommand\literals{\LITSYM}
\newcommand \lit        {\literals\sig\V}
\newcommand \Xlit       {\literals\sig\X}
\newcommand \Ylit       {\literals\sig\Y}
\mathcommand\GENLITSYM{\GENSYM\hspace{-.08em}\LITSYM}
\mathdoubleapplycommand\genliterals{\GENLITSYM}
\newcommand \genlit        {\genliterals\sig\V}
\newcommand \Xgenlit       {\genliterals\sig\X}
\newcommand \Ygenlit       {\genliterals\sig\Y}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

headernamesrest.tex
% FILE: headernamesrest.tex
% CONTENTS: CP's standard file for including world knowledge,
%           such as names, language, characters, life times.
%
% This file must be loadable as the first file of any latex file!
% So do not use any extensions which are not contained in it,
% such as \mathcommand
%
% Moreover, \emph must not be used here!

\newcommand\namefont{}
\newcommand\bibcrit[1]{\ {\sl{(#1)}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{url}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\hyphenation{
ab-brevi-a-tion
ab-brevi-a-tions
ab-ge-leitete
ab-ge-leitetem
ab-ge-leiteten
ab-ge-leiteter
ab-ge-leitetes
ab-weicht
accord-ing
Acker-mann
actual
actual-ly
Akten-zeichen
aktiv
aktive
aktivem
aktiven
aktiver
aktives
although
always
ana-logous-ly
analysis
an-ge-mie-te-ten
annota-tions
announced
ante-cedent
ante-cedents
antici-pa-tion
appli-ca-tion
appli-ca-tions
area
areas
argu-ment
aspect
asser-tion
asser-tions
assump-tion
assump-tions
Aus-wahl-funktion
Aus-spra-che
author
authors
auto-ma-ted
auto-ma-tion
auto-ma-tisch
auto-ma-ti-sche
auto-ma-ti-schem
auto-ma-ti-schen
auto-ma-ti-scher
auto-ma-ti-sches
Autoren
axio-ma-tics
axiom
Axiome
axioms
basic
basis
be-ein-flusst
be-endet
beharr-lich
being
be-kannte
be-kanntem
be-kannten
be-kannter
be-kanntes
be-rech-tig-te
Bereich
Be-rei-chen
beside
besides
be-zeich-net
Be-zeich-nung
bietet
bis-heri-gen
certain
che-mi-sche
che-mi-schem
che-mi-schen
che-mi-sches
che-mi-scher
com-pati-bi-lity
classi-fi-ca-tion
concept
con-struc-tor
corol-lary
counter-example
counter-examples
creati-vity
custom-ary
Dag-stuhl
define
defi-niert
defi-nierte
defi-niertem
defi-nierten
defi-nierter
defi-niertes
defi-nit
defi-nite
defi-nitem
defi-niten
defi-niter
defi-nites
defi-ni-tion
defi-ni-tions
de-monstra-tion
denen
der-arti-ge
der-arti-gen
der-arti-gem
der-arti-ger
der-arti-ges
De-signs
des-cente
descent
deter-mined
deutsche
deutschem
deutschen
deutscher
deutsches
develop-ing
deviate
diese
direc-tion
dis-equality
dis-equali-ties
dis-respected
domain
durch-aus
Effi-zienz
easily
effec-tive
ehren-amt-licher
ehren-amt-liches
ehren-amt-liche
ehren-amt-lichen
ehren-amt-lichem
eigent-lichen
Ein-arbei-tung
eine
einem
einen
einer
eines
either
elek-tro-ni-scher
elek-tro-ni-sches
elek-tro-ni-sche
elek-tro-ni-schen
elek-tro-ni-schem
element
elements
elemen-tary
em-pfohlen
em-pfun-dener
em-pfun-denes
em-pfun-dene
em-pfun-denen
em-pfun-denem
enforce
enforced
enforces
eng-lisch
Engli-scher
Engli-sches
Engli-sche
Engli-schen
Engli-schem
englisch-sprachig
englisch-sprachi-ge
englisch-sprachi-gem
englisch-sprachi-gen
englisch-sprachi-ger
englisch-sprachi-ges
English
entitled
epsi-lon
equi-valent
equi-valence
especial-ly
essay
essays
essen-tial
estab-lish
estab-lished
evaluation
every
exist-ence
existie-ren
existiert
existier-te
existier-ten
explain
explained
ex-plicit-ly
Ent-deckung
ent-schul-di-gen
Ent-wick-lung
Ent-wick-lun-gen
Ent-wurf
etab-lier-ter
etwas
every-where
exami-na-tion
exist
ex-peri-ence
Ex-peri-mente
existen-tial
extra-pola-tion
fach-wissen-schaft-liche
fach-wissen-schaft-lichen
Fach-be-reich
Fahr-zeu-gen
Falsi-fi-ka-tion
father
figure
final
finally
finite
finitis-tic
focus
forma-tion
formula
founda-tions
frequent
frequent-ly
further-more
general
ge-sicher-te
ge-sicher-tem
ge-sicher-ten
ge-sicher-ter
ge-sicher-tes
Ge-werk-schaft
glei-chen
Glei-chung
Glei-chun-gen
geo-metry
Geo-metrie
Gesamt-komplex
ge-sehen
Gestalt
grie-chi-sche
grie-chi-schem
grie-chi-schen
grie-chi-scher
grie-chi-sches
groun-ded-ness
glo-bal-ly 
Grund-lage
Grund-lagen
Grund-lagen-wissen-schaft 
Grund-lagen-wissen-schaf-ten 
guaran-tee-ing
Haltung
haupt-ver-ant-wort-lich
Haupt-ver-ant-wort-liche
Haupt-ver-ant-wort-lichem
Haupt-ver-ant-wort-lichen
Haupt-ver-ant-wort-licher
Haupt-ver-ant-wort-liches
have
% Herbrand
hin-rei-chend
hin-rei-chen-de
hin-rei-chen-dem
hin-rei-chen-den
hin-rei-chen-der
hin-rei-chen-des
human
humans
hyper-text
Hyper-texte
hypo-theses
hypo-thesis
hypo-the-size
hypo-the-sizing
idealis-ti-sche
idealis-ti-schem
idealis-ti-schen
idealis-ti-scher
idealis-ti-sches
ideali-za-tion
ihre
ihrem
ihren
ihrer
ihres
indeed
in-definite
index-ed
Induk-tions-be-wei-ser
Induk-tions-ord-nun-gen
Inferenz-systeme
in-finie
in-finite
in-formatics
inner-most
ins-ge-samt
inter-action
inter-connec-tion
inter-connec-tions
interest
inter-medi-ate
inter-pre-ta-tion
intro-duc-tion
intro-duc-tions
irreflexive
Jahres-tref-fen
je-weils
Kai-sers-lau-tern
Kaplan
Kenn-zeichen
kenn-zeich-net
knowledge
knowledge-able
klassi-sche
klassi-schen
klassi-schem
klassi-scher
konnte
Kritik
kriti-sche
kriti-schen
kriti-schem
kriti-scher
kriti-sches
Kumu-la-tion
latter
leistet
lesen
little
logic
logics
logi-sche
logi-schen
logi-schem
logi-scher
logi-sches
magni-tude
mani-fold
mani-folds
mani-pu-la-tion
mathe-ma-tica
mathe-ma-tical
mathe-ma-tician
mathe-ma-ticians
mathe-ma-tics
mathe-ma-ti-cal-ly
Mathe-ma-tik
mathe-ma-ti-sche
mathe-ma-ti-schem
mathe-ma-ti-schen
mathe-ma-ti-scher
mathe-ma-ti-sches
method
methods
metho-di-cal
methodo-logi-sche
methodo-logi-schen
methodo-logi-schem
methodo-logi-scher
methodo-logi-sches
micro-processor
micro-processors
Mie-ter
Modell-klasse
model
models
modern
moder-ne
moder-nem
moder-nen
moder-ner
moder-nes
mono-toni-city
mora-lisch
mora-li-sche
mora-li-schen
mora-li-schem
mora-li-scher
mora-li-sches
micro-pro-cessor
Mieter-sache
Miet-gebrauch
Miet-vertrag
Miet-vertrages
mini-mum
mis-anthropic
mis-under-stood
mis-under-standing
mitt-lere
Musik
Nach-mieterin
natu-ral
Natur-wissen-schaft
Natur-wissen-schaf-ten
Neben-kosten
nega-tiv
nega-tive
neo-logism
never-the-less
Nomina-list
Nomina-listen
notable
nothing
notion
numeral
numer-i-cal
Ober-begriff
object
objects
Objekt
occur
occur-rence
occur-ren-ces
ohne
onto-logisch
onto-logi-sche
onto-logi-schem
onto-logi-schen
onto-logi-scher
onto-logi-sches
operationali-zation
order
Origi-nal
Origi-nals
Origi-nal-zitate
organi-sa-to-risch
organi-sa-to-ri-sche
organi-sa-to-ri-schem
organi-sa-to-ri-schen
organi-sa-to-ri-scher
organi-sa-to-ri-sches
other-wise
para-digm
Para-digma
Para-digmas
para-digms
Parallelen-axiom
para-meter
para-meters
parti-ci-pa-tion
philo-so-phisch
philo-so-phi-sche
philo-so-phi-schem
philo-so-phi-schen
philo-so-phi-scher
philo-so-phi-sches
philo-sophy
parallel
partial-i-ty
poly-nomial
poly-nomials
posi-tiv
posi-tive
post-humously
product
pro-posi-tion
pro-posi-tions
pro-posi-tio-nal
ratio-nalis-mus
ratio-nalis-tisch 
ratio-nalis-tische 
ratio-nalis-tischem 
ratio-nalis-tischen 
ratio-nalis-tischer 
ratio-nalis-tisches 
really
Real-wissen-schaf-ten
recht-eckige
recht-eckigem
recht-eckigen
recht-eckiger
recht-eckiges
re-cog-nition
re-duci-bi-lity
Re-duk-tions-re-la-tion
regard-less
Regel
relation
relation-ship
relation-ships
re-organi-za-tion
repeti-tion
replace
represent
represents
represen-ted
represen-ting
repre-sen-ta-tion
require
requires
reso-lu-tion
restric-tive
result
Rhein-steig
Sammel-bezeich-nung 
schrift-lich
schwerere
Schwierig-keiten
second
seiten-gleich
seiten-gleiche
seiten-gleichem
seiten-gleichen
seiten-gleiches
seiten-gleicher
seman-tic
seman-tics
separa-tion
sequence
sequen-ces
several
sinn-voller
sitt-lich
sitt-liche
sitt-lichem
sitt-lichen
sitt-liches
sitt-licher
speaking
solu-tion
solu-tions
sophis-ti-ca-tion
Spezi-fi-ka-tio-nen
Spezi-fi-ka-tions-sprache
Sko-lem-i-za-tion
simpli-fi-cation
speci-fi-ca-tion
speci-fi-ca-tions
speci-fier
speci-fied
stable
straight-forward
sub-sequent
super-fluous
sym-metrical
sym-metrical-ly
tauto-logy
taking
tertium
theorem
theorems
Theorie
Theorien
theory
theo-re-ti-sche
theo-re-ti-schen
theo-re-ti-schem
theo-re-ti-sches
theo-re-ti-scher
thesis
topo-logy
total
trans-cend
typischer-weise
un-answer-ed
un-bestimmt
un-bestimmte
un-bestimm-tem
un-bestimm-ten
un-bestimm-ter
un-bestimm-tes
under
under-stand
under-stands
under-stood
unless
Un-par-tei-lich-keit
unter-bewusst
unter-schied
until
ur-element
ur-elements
Ur-sache
usage
valid-i-ty
values
ver-an-lasst
Ver-an-stal-tung
Ver-bin-dung
ver-brei-ter-tem
Ver-mieters
Ver-mie-terin
ver-pflich-te-te
viel-leicht
Vien-na
Vor-annahme
Vor-annahmen
vor-kom-men-den
vor-para-dig-ma-ti-schen
vor-para-dig-ma-ti-scher
Vor-schrif-ten
wahr-ge-nom-men
weder
wei-te-ren
Weni-ger-ver-brauchs
wesent-liche
wesent-lichem
wesent-lichen
wesent-liches
wesent-licher
Win-kel
Wissen-schaft
Wissen-schaften
Wissen-schaft-ler
Wissen-schaft-lern
wissen-schaft-liche
wissen-schaft-lichen
wissen-schaft-licher
wissen-schaft-liches
Wissen-schafts-ent-wick-lung
wurde
zahl-reiche
zahl-reichen
zahl-reichem
zahl-reicher
zahl-reiches
zu-neh-men-den
zu-gleich
Zeich-nun-gen
zwei-sprachi-ge
zwei-sprachi-gem
zwei-sprachi-gen
zwei-sprachi-ger
zwei-sprachi-ges
Zweit-woh-nungs-steu-er
zwischen
}

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FIRST NAMES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand\achilles {Achille\es} % both German and English spelling
\newcommand\adolf    {Adolf}
\newcommand\alan     {Alan}
\newcommand\albert   {Al\-bert}
\newcommand\alexander{Alex\-ander}
\newcommand\alfred   {Alfred}
\newcommand\andreas  {An\-dre\-a\es}
\newcommand\andrew   {An\-drew}
\newcommand\anne     {Anne}
\newcommand\bernd    {Bernd}
\newcommand\bernard  {Bernard}
\newcommand\bernhard {Bern\-hard}
\newcommand\benjamin {Benjamin}
\newcommand\carl     {Carl}
\newcommand\carlos   {Car\-lo\es}
\newcommand\carsten  {Car\esi ten}
\newcommand\catherine{{\namefont Catherine}}
\newcommand\charles  {Charle\es}
\newcommand\charybdis{Charybdi\es}
\newcommand\christian{Christian}
\newcommand\christoph{Christoph}
\newcommand\claude   {Claude}
\newcommand\claus    {Clau\es}
\newcommand\david    {{\namefont David}}
\newcommand\donald   {Donald}
\newcommand\dieter   {Dieter}
\newcommand\dirk     {Dirk}
\newcommand\edmund   {\mbox{Edmund}}
\newcommand\edgar    {\mbox{Edgar}}
\newcommand\edward   {\mbox{Edward}}
\newcommand\emmy     {{\namefont Emmy}}
\newcommand\emil     {{\namefont Emil}}
\newcommand\ernest   {Ernest}
\newcommand\ernst    {Ernst}
\newcommand\ferdinand{Ferdinand}
\newcommand\francois {Fran\-\c coi\es}
\newcommand\friedrich{Fried\-rich}
\newcommand\frank    {Frank}
\newcommand\gabriel  {Gabri\ewithtrema l}
\newcommand\gerhard  {Ger\-hard}
\newcommand\georg    {Georg}
\newcommand\george   {George}
\newcommand\gerd     {Gerd}
\newcommand\gottlob  {{\namefont Gott\-lob}}
\newcommand\gottfried{{\namefont Gott\-fried}}
\newcommand\gustav   {Gustav}
\newcommand\hans     {Han\es}
\newcommand\helmut   {Hel\-mut}
\newcommand\heinrich {Hein\-rich}
\newcommand\henk     {Henk}
\newcommand\henry    {{\namefont Henry}}
\newcommand\henrik   {Henrik}
\newcommand\herbert  {Her\-bert}
\newcommand\hermann  {Her\-mann}
\newcommand\horst    {Horst}
\newcommand\howard   {{\namefont Howard}}
\newcommand\hubert   {Hubert}
\newcommand\immanuel {Immanu\ewithtrema l}
\newcommand\immanuelwithouttrema{Immanuel}
\newcommand\irving   {Irving}
\newcommand\ismael   {Isma\ewithtrema l}
\newcommand\jacques  {{\namefont Jacque\es}}
\newcommand\james    {Jame\es}
\newcommand\jan      {Jan}
\newcommand\joachim  {Jo\-achim}
\newcommand\joerg    {J\oe rg}
\newcommand\johan    {Jo\-han}
\newcommand\johann   {{\namefont Johann}}
\newcommand\jose     {Jos\'e}
\newcommand\joseph   {Joseph}
\newcommand\juergen  {J\ue r\-gen}
\newcommand\jean     {Jean}
\newcommand\john     {John}
\newcommand\julius   {Julius}
\newcommand\karl     {Karl}
\newcommand\kazimierz{Kazimierz}
\newcommand\klaus    {Klau\es}
\newcommand\konrad   {Kon\-rad}
\newcommand\kurt     {Kurt}
\newcommand\lawrence {Lawrence}
\newcommand\leon     {Leon}
\newcommand\leopold  {Leo\-pold}
\newcommand\ludwig   {Lud\-wig}
\newcommand\magdalena{Magda\-lena}
\newcommand\manfred  {Man\-fred}
\newcommand\maurice  {{\namefont Maurice}}
\newcommand\maxchristiannamenonamefont{Max} %% \max is already a tex command
\newcommand\maxchristianname{{\namefont\maxchristiannamenonamefont}}
\newcommand\markus   {Mar\-ku\es}
\newcommand\martin   {{\namefont Mar\-tin}}
\newcommand\marvin   {{\namefont Mar\-vin}}
\newcommand\matthias {Matthia\es}
\newcommand\michael  {Micha\-\ewithtrema l}%{Mi\-cha\-\ewithtrema l}
\newcommand\michaelwithouttrema{Micha\-el}%{Mi\-cha\-el}
\newcommand\nicolaus {Ni\-co\-lau\es}
\newcommand\ottonoconflict{Ot\-to}
\newcommand\paolo    {Paolo}
\newcommand\paul     {{\namefont Paul}}
\newcommand\peter    {Peter}
\newcommand\pierre   {Pierre}
\newcommand\raymond  {Raymond}
\newcommand\rene     {Ren\'e}
\newcommand\redcap   {Red\-cap}
\newcommand\richard  {Ri\-chard}
\newcommand\robert   {Ro\-bert}
\newcommand\robin    {Robin}
\newcommand\roland   {Ro\-land}
\newcommand\rudolf   {Ru\-dolf}
\newcommand\ruediger {R\ue\-di\-ger}
\newcommand\scylla   {Scylla}
\newcommand\sergey   {Ser\-gey}
\newcommand\stanislaw{Stanis\l aw}
\newcommand\stanley  {Stan\-ley}
\newcommand\stephan  {Ste\-phan}
\newcommand\thomas   {Tho\-ma\es}
\newcommand\thoralf  {{\namefont Thoralf}}
\newcommand\tobias   {{\namefont To\-bi\-a\es}}
\newcommand\wolfgang {Wolf\-gang}
\newcommand\ulrich   {Ul\-rich}
\newcommand\ulysses  {Ulysse\es}
\newcommand\uwe      {Uwe}
\newcommand\vladimir {Vla\-di\-mir}
\newcommand\volker   {\mbox{Vol\-ker}}
\newcommand\warren   {Warren}
\newcommand\werner   {Wer\-ner}
\newcommand\wilfried {Wil\-fried}
\newcommand\wilhelm  {\mbox{Wilhelm}}
\newcommand\william  {Will\-iam}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% SCIENTISTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand\aanderaa        {{\namefont Aanderaa}}
\newcommand\aanderaaname    {{\namefont St\aa l \aanderaa}}
\newcommand\abelindex       {\index{Abel, Niels Henrik (1802--1829)}}
\newcommand\abel            {{\namefont Abel}}
\newcommand\abelname        {{\namefont Niel\es\ \henrik\ \abel}} % verified
\newcommand\abellifetime    {(1802--1829)} % verified
\newcommand\acerbiindex     {\index{Acerbi, Fabio}}
\newcommand\acerbi          {{\namefont Acerbi}}
\newcommand\acerbiname      {\acerbiindex{\namefont Fabio \acerbi}}
\newcommand\ackermannindex  {\index{Ackermann, Wilhelm (1896--1962)}}
\newcommand\protectedackermannindex
                            {\protect\index{Ackermann, Wilhelm (1896--1962)}}
\newcommand\ackermann
                   {{\namefont A\nolinebreak\hskip-.07em\nolinebreak cker\-mann}}
\newcommand\ackermannname   {\ackermannindex{\namefont \wilhelm\ \ackermann}}
\newcommand\ackermannlifetime{(1896--1962)}
\newcommand\ackermannfunction{\index{Ackermann function}\ackermann\ function}
\newcommand\aczel           {{\namefont Aczel}}
\newcommand\aczelname       {{\namefont \peter\ \aczel}}
\newcommand\adorno          {Adorno}
\newcommand\adornoname      {Theodor W. \adorno}
\newcommand\ahrendt         {{\namefont Ahrendt}}
\newcommand\ahrendtname     {{\namefont\wolfgang\ \ahrendt}}
\newcommand\ajdukiewiczindex{\index{Ajdukiewicz, Kazimierz (1890--1963)}}
\newcommand\ajdukiewicz     {{\namefont Ajdukiewicz}}
\newcommand\ajdukiewiczname{\ajdukiewiczindex{\namefont\kazimierz\ \ajdukiewicz}}
\newcommand\ajdukiewiczlifetime{(1890--1963)}
\newcommand\anellisindex    {\index{Anellis, Irving H. (1946--2013)}}
\newcommand\protectedanellisindex
                            {\protect\index{Anellis, Irving H. (1946--2013)}}
\newcommand\anellis         {{\namefont Anelli\es}}
\newcommand\anellisname     {{\namefont\anellisindex\irving\ H. \anellis}}
\newcommand\anellisarchives {\anellis\ Archives\index{Anellis Archives}}
\newcommand\anellislifetime {(1946--2013)}
\newcommand\albertus        {{\namefont Albertu\es}}
\newcommand\albertusname    {{\namefont\albertus\ Magnu\es}}
\newcommand\albertuslifetime{(\ca\,1200--1280)}
\newcommand\anselm          {{\namefont Anselmu\es}}
\newcommand\anselmname      {{\namefont\anselm\ Cantuariensi\es}}
\newcommand\anselmlifetime  {(1033--1109)}
\newcommand\archimedes      {{\namefont Archimedes}}
\newcommand\archimedesname  {{\namefont\archimedes\ of Syracuse}}
\newcommand\archimedean     {Archimedean}
\newcommand\archimedeanaxiom{\index{Archimedean Axiom}\archimedean\ Axiom}
\newcommand\artinindex      {\index{Artin, Emil (1898--1962)}}
\newcommand\protectedartinindex      
                    {\protect\index{Artin, Emil (1898--1962)}}
\newcommand\artin           {{\namefont Artin}}
\newcommand\artinname       {\artinindex{\namefont \emil\ \artin}}
\newcommand\artinlifetime   {(1898--1962)}
\newcommand\aristotleindex  {\index{Aristotle (384--322\,\BC)}}
\newcommand\aristotle       {{\namefont Ari\esi totle}}
\newcommand\aristotlename   {{\namefont\aristotle\ of Stagira}}
\newcommand\aristotlelifetime{(384--322\,\BC)}
\newcommand\aristotelian    {{\namefont Ari\esi totelian}}
\newcommand\aristotelianlogicindex{\index{Aristotelian logic}}
\newcommand\aristotelianlogic{\aristotelianlogicindex\aristotelian\ logic}
\newcommand\aristotelisch   {{\namefont Ari\esi totelisch}}
\newcommand\aristoteles     {{\namefont Ari\esi toteles}}
\newcommand\aristotelesname {{\namefont Ari\esi toteles von Stagira}}
\newcommand\aristoteleslifetime{(384--322\,v.\,Chr.)}
\newcommand\armando         {Armando}
\newcommand\armandoname     {Alessandro \armando}
\newcommand\arndt           {{\namefont Arndt}}
\newcommand\hanswernerarndtname{{\namefont\hans\ \werner\ \arndt}}
\newcommand\asser           {{\namefont Asser}}
\newcommand\assername       {{\namefont G\ue nter \asser}}
\newcommand\asserlifetime   {(*1926)}
\newcommand\andrewsindex    {\index{Andrews, Peter B. (*1937)}}
\newcommand\andrewsindexbegin{\index{Andrews, Peter B. (*1937)|(}}
\newcommand\andrewsindexend {\index{Andrews, Peter B. (*1937)|)}}
\newcommand\protectedandrewsindex{\protect\index{Andrews, Peter B. (*1937)}}
\newcommand\andrews         {\mbox{\namefont Andrew\es}}
\newcommand\andrewsname     {\andrewsindex{\namefont\peter\ B. \andrews}}
\newcommand\andrewsnamewithoutmiddleinitial
                            {\andrewsindex{\namefont\peter\ \andrews}}
\newcommand\andrewslifetime {(*1937)}
\newcommand\anscombeindex   {\index{Anscombe, G. E. M. (1919--2001)}}
\newcommand\anscombe        {\mbox{\namefont Anscombe}}
\newcommand\anscombename    {{\namefont G. E. M. \anscombe}}
\newcommand\anscombelifetime{(1919--2001)}
\newcommand\augustinus      {{\namefont Augu\esi tinus}}
\newcommand\augustinusname  {{\namefont \augustinus\ Hipponensis}}
\newcommand\augustinuslifetime{(354--430)}
\newcommand\aubinindex      {\index{Aubin, Raymond}}
\newcommand\protectedaubinindex{\protect\index{Aubin, Raymond}}
\newcommand\aubin           {\mbox{\namefont Aubin}}
\newcommand\aubinname       {\aubinindex{\namefont\raymond\ \aubin}}
\newcommand\aubinnamewithoutmiddleinitial{{\namefont\peter\ \aubin}}
\newcommand\autexierindex   {\index{Autexier, Serge (*1971)}}
\newcommand\protectedautexierindex{\protect\index{Autexier, Serge (*1971)}}
\newcommand\autexier        {\mbox{\namefont Autexier}}
\newcommand\autexiername    {\autexierindex{\namefont Serge \autexier}}
\newcommand\autexierlifetime{(*1971)}
\newcommand\avenhaus        {{\namefont Aven\-hau\es}}
\newcommand\avenhausname    {{\namefont\juergen\ \avenhaus}}
\newcommand\avron           {{\namefont Avron}}
\newcommand\avronname       {{\namefont Arnon \avron}}
\newcommand\awodey          {{\namefont Awodey}}
\newcommand\awodeyname      {{\namefont Steve \awodey}}
\newcommand\baaz            {{\namefont Baaz}}
\newcommand\baazname        {{\namefont\matthias\ \baaz}}
\newcommand\babbage         {Babbage}
\newcommand\babbagename     {\charles\ \babbage}
\newcommand\babbagelifetime {(1792--1871)}
\newcommand\bach            {Bach}
\newcommand\bachname        {Emmon \bach}
\newcommand\bachetindex     {\index
                             {Bachet de M\'eziriac, Claude Gaspard (1581--1638)}}
\newcommand\bachet          {{\namefont Bachet}}
\newcommand\bachetname      {\bachetindex
                             {\namefont\claude\ Gaspard \bachet\ de M\'eziriac}}
\newcommand\bachetlifetime  {(1581--1638)}
\newcommand\bachmair        {Bach\-mair}
\newcommand\bachmairname    {Leo \bachmair}
\newcommand\backhouse       {Backhouse}
\newcommand\backhousename   {\roland\ \backhouse}
\newcommand\bacon           {Bacon}
\newcommand\baconname       {Franci\es\ \bacon}
\newcommand\barendregt      {{\namefont Barendregt}}
\newcommand\barendregtname  {{\namefont Hen(dri)k P. \barendregt}}
\newcommand\barnerindex     {\index{Barner, Klaus}}
\newcommand\protectedbarnerindex{\protect\index{Barner, Klaus}}
\newcommand\barner          {{\namefont Barner}}
\newcommand\barnername      {\barnerindex{\namefont\klaus\ \barner}}
\newcommand\barwise         {{\namefont Barwise}}
\newcommand\barwisename     {{\namefont Jon \barwise}}
\newcommand\basinindex      {\index{Basin, David}}
\newcommand\protectedbasinindex{\protect\index{Basin, David}}
\newcommand\basin           {{\namefont Basin}}
\newcommand\basinname       {\basinindex{\namefont\david\ \basin}}
\newcommand\bauermengelbergindex{\index{Bauer-Mengelberg, Stefan (1927--1996)}}
\newcommand\bauermengelberg {{\namefont Bauer-Mengelberg}}
\newcommand\bauermengelbergname
                       {\bauermengelbergindex{\namefont Stefan \bauermengelberg}}
\newcommand\bauermengleberglifetime{(1927--1996)}
\newcommand\baumgartner     {Baum\-gart\-ner}
\newcommand\baumgartnername {\peter\ \baumgartner}
\newcommand\bayes           {{\namefont Bayes}}
\newcommand\bayesname       {{\namefont\thomas\ \bayes}}
\newcommand\bayeslifetime   {(1701--1761)}
\newcommand\becker          {{\namefont Becker}}
\newcommand\beckername      {{\namefont\klaus\ \becker}}
\newcommand\beckert         {{\namefont Beckert}}
\newcommand\beckertname     {{\namefont\bernhard\ \beckert}}
\newcommand\bell            {Bell}
\newcommand\bellname        {\john\ Lane \bell}
\newcommand\beethoven       {Beethoven}
\newcommand\beethovenname   {\ludwig\ van \beethoven}
\newcommand\beethovenlifetime{(1770--1827)}
\newcommand\behmannindex    {\index{Behmann, Heinrich (1891--1970)}}
\newcommand\behmann         {{\namefont Behmann}}
\newcommand\behmannname     {\behmannindex{\namefont\heinrich\ \behmann}}
\newcommand\behmannlifetime {(1891--1970)}
\newcommand\behnkeindex     {\index{Behnke, Heinrich (1898--1979)}}
\newcommand\behnke          {{\namefont Behnke}}
\newcommand\behnkename      {\behnkeindex{\namefont\heinrich\ \behnke}}
\newcommand\behnkelifetime  {(1898--1979)}
\newcommand\bendix          {Bendix}
\newcommand\bendixname      {P. B. \bendix}
\newcommand\benzmuellerindex{\index
            {Benzmueller, Christoph (*1968)@{Benzm\"uller, \christoph\ (*1968)}}}
\newcommand\protectedbenzmuellerindex{\protect\index
            {Benzmueller, Christoph (*1968)@{Benzm\"uller, \christoph\ (*1968)}}}
\newcommand\benzmueller     {{\namefont Benz\-m\ue ller}}
\newcommand\benzmuellername{\benzmuellerindex{\namefont\christoph\ \benzmueller}}
\newcommand\benzmuellerlifetime{(*1968)}
\newcommand\berghammer      {Berg\-hammer}
\newcommand\berghammername  {\rudolf\ \berghammer}
\newcommand\bergstra        {{\namefont Bergstra}}
\newcommand\bergstraname    {{\namefont\jan\ A. \bergstra}}
\newcommand\berkeley        {{\namefont Berkeley}}
\newcommand\berkeleyname    {{\namefont \george\ \berkeley}}
\newcommand\berkeleylifetime{(1685--1753)}
\newcommand\protectedbernaysindex{\protect\index{Bernays, Paul (1888--1977)}}
\newcommand\bernaysindex    {\index{Bernays, Paul (1888--1977)}}
\newcommand\bernaysindexbegin{\index{Bernays, Paul (1888--1977)|(}}
\newcommand\bernaysindexend {\index{Bernays, Paul (1888--1977)|)}}
\newcommand\bernays         {\mbox{\namefont Ber\-nay\es}}
\newcommand\bernaysname     {\bernaysindex{\namefont \paul\       \bernays}}
%                           {             {\namefont \paul\ Isaak \bernays}}
\newcommand\bernaysschoenfinkel{\bernays--\schoenfinkel}
\newcommand\bernayslifetime {(1888--1977)}
\newcommand\bernsteinindex  {\index{Bernstein, Felix (1878--1956)}}
\newcommand\bernstein       {{\namefont Bernstein}}
\newcommand\bernsteinname   {\bernsteinindex{\namefont Felix \bernstein}}
\newcommand\bernsteinlifetime{(1878--1956)}
\newcommand\bertling        {{\namefont Bertling}}
\newcommand\bertlingname    {{\namefont\hubert\ \bertling}}
\newcommand\bevers          {Bever\es}
\newcommand\beversname      {Eddy \bevers}
\newcommand\bibel           {{\namefont Bi\-bel}}
\newcommand\bibelname       {{\namefont\wolfgang\ \bibel}}
\newcommand\billy           {{\namefont Billy}}
\newcommand\billyname       {{\namefont\jacques\ de \billy}}
\newcommand\billylifetime   {(1602--1679)}
\newcommand\bledsoeindex    {\index{Bledsoe, W. W. (1921--1995)}} 
\newcommand\bledsoe         {{\namefont Bledsoe}}
\newcommand\bledsoename     {\bledsoeindex{\namefont W.\,W.\,\,\bledsoe}}
% Real name is Woodrow Wilson Bledsoe. Nickname Woody. But he wanted W. W.!
\newcommand\bledsoelifetime {(1921--1995)}
\newcommand\bobzien         {{\namefont Bobzien}}
\newcommand\bobzienname     {{\namefont Susanne \bobzien}}
\newcommand\boenert         {{\namefont Boe\-nert}}
\newcommand\boenertname     {{\namefont Detlev \boenert}}
\newcommand\bohr            {{\namefont Bohr}}
\newcommand\bohrname        {{\namefont Nil\es\ \bohr}}
\newcommand\bolzano         {{\namefont Bolzano}}
\newcommand\bolzanoname     {{\namefont\bernard\ \bolzano}}
\newcommand\bolzanolifetime {(1781--1848)}
\newcommand\bookhade        {Bookhade}
\newcommand\bookhadename    {\robert\ \bookhade}
\newcommand\boole           {{\namefont Boole}}
\newcommand\boolename       {{\namefont\george\ \boole}}
\newcommand\boolelifetime   {(1815--1864)}
\newcommand\myboolean       {\boole an}
\newcommand\myBoolean       {\boole an}
\newcommand\boolosindex                 {\index{Boolos, George (1940--1996)}}
\newcommand\protectedboolosindex{\protect\index{Boolos, George (1940--1996)}}
\newcommand\boolos          {{\namefont Boolos}}
\newcommand\boolosname      {\boolosindex{\namefont\george\ \boolos}}
\newcommand\booloslifetime  {(1940--1996)}
\newcommand\bornindex       {\index{Born, Max (1882--1970)}}
\newcommand\born            {{\namefont Born}}
\newcommand\bornname        {\bornindex{\namefont\maxchristianname\ \born}}
\newcommand\bornlifetime    {(1882--1970)}
\newcommand\bouhoula        {Bou\-hou\-la}
\newcommand\bouhoulaname    {Adel \bouhoula}
\newcommand\bourbakiindex   {\index{Bourbaki, Nicolas (pseudnoym)}}
\newcommand\protectedbourbakiindex{\protect\index{Bourbaki, Nicolas (pseudonym)}}
\newcommand\bourbaki        {{\namefont Bourbaki}}
\newcommand\bourbakiname    {\bourbakiindex{\namefont Nicola\es\ \bourbaki}}
\newcommand\boyerindex      {\index{Boyer, Robert S. (*1946)}}
\newcommand\boyer           {{\namefont Boyer}}
\newcommand\boyername       {\boyerindex{\namefont\robert\ S. \boyer}}
\newcommand\boyerswifename  {{\namefont\anne\ O. \boyer}}
\newcommand\boyerlifetime   {(*1946)}
\newcommand\boyermoore      {\boyerindex\mooreindex\boyer--\moore}
\newcommand\boyermooretheoremproversindex{\index{Boyer--Moore theorem provers}}
\newcommand\boyermooretheoremprover
                      {\boyermooretheoremproversindex\boyermoore\ theorem prover}
\newcommand\boyermooreTheoremProver
                      {\boyermooretheoremproversindex\boyermoore\ Theorem Prover}
\newcommand\boyermooretheoremprovers{\boyermooretheoremprover s}
\newcommand\boyermoorewaterfallindex{\index{Boyer--Moore waterfall}}
\newcommand\boyermoorewaterfall{\boyermoorewaterfallindex\boyermoore\ waterfall}
\newcommand\boyermooreWaterfall{\boyermoorewaterfallindex\boyermoore\ Waterfall}
\newcommand\boyermooremachines
                            {\index{Boyer--Moore machines}\boyermoore\ machines}
\newcommand\bmfssapindex
                  {\protect\index{Boyer--Moore fast string searching algorithm}}
\newcommand\brahe           {Brahe}
\newcommand\brahename       {Tyge \brahe}%{Tyge B. \brahe}
\newcommand\brahelifetime   {(1546--1601)}
\newcommand\brentano        {{\namefont Brentano}}
\newcommand\brentanopoetname{{\namefont Clemens \brentano}}
\newcommand\brentanopoetlifetime{(1778--1842)}
\newcommand\brentanophilosophername{{\namefont Franz \brentano}}
\newcommand\brentanophilosopherlifetime{(1838--1917)}
\newcommand\brockindex      {\index{Brock, Bishop}}
\newcommand\brock           {{\namefont Brock}}
\newcommand\brockname       {\brockindex{\namefont Bishop \brock}}
\newcommand\bronsard        {{\namefont Bronsard}}
\newcommand\bronsardname    {{\namefont\francois\ \bronsard}}
\newcommand\brotherston     {{\namefont Brotherston}}
\newcommand\brotherstonname {{\namefont\james\ \brotherston}}
\newcommand\brouwersecondname{Brouwer} % Not: Brouwers (as often written)
\newcommand\brouwerfirstname{L.\,\,E.\,\,J.}
%{Luitzen}
%{Luitzen E. J.}
%Parsons: Also, Brouwer always referred to himself in print as L. E. J. Brouwer; that is the way most other writers have referred to him.  I don't know if anyone called him Luitzen; from van Dalen's biography, it is clear that he was known familiarly as Bertus (after Egbertus, his second Christian name).
\newcommand\brouwerindex    {\index{Brouwer, L. E. J. (1881--1966)}}
\newcommand\protectedbrouwerindex{\protect\index{Brouwer, L. E. J. (1881--1966)}}
\newcommand\brouwer         {{\namefont \brouwersecondname}}
\newcommand\brouwername     
                {\brouwerindex{\namefont \brouwerfirstname\ \brouwersecondname}}
\newcommand\brouwerlifetime {(1881--1966)}
\newcommand\brownchad       {{\namefont Brown}}
\newcommand\brownchadname   {{\namefont Chad E. \brownchad}}
\newcommand\broy            {Broy}
\newcommand\broyname        {\manfred\ \broy}
\newcommand\bruggaier       {Bruggaier}
\newcommand\bruggaiername   {Juliana \bruggaier}
\newcommand\bruijn          {Bruijn}
\newcommand\bruijnname      {Nicolaa\es\ Govert de \bruijn}
\newcommand\buchholz        {{\namefont Buch\-holz}}
\newcommand\buchholzname    {{\namefont\wilfried\ \buchholz}}
\newcommand\buchholzlifetime{(*1948)}
\newcommand\buechi          {{\namefont B\ue chi}}
\newcommand\buechiname      {{\namefont\julius\ \richard\ \buechi}}
\newcommand\buechilifetime  {(1924--1984)}
\newcommand\buerckert       {B\ue rckert}
\newcommand\buerckertname   {\hans-\juergen\ \buerckert}
\newcommand\buldtindex                 {\index{Buldt, Bernd}}
\newcommand\protectedbuldtindex{\protect\index{Buldt, Bernd}}
\newcommand\buldt           {{\namefont Buldt}}
\newcommand\buldtname       {\buldtindex{\namefont \bernd\ \buldt}}
\newcommand\bundyindex      {\index{Bundy, Alan (*1947)}}
\newcommand\protectedbundyindex{\protect\index{Bundy, Alan (*1947)}}
\newcommand\bundy           {{\namefont Bundy}}
\newcommand\bundynamenoindex{{\namefont\alan\ \bundy}}
%                           {{\namefont\alan\ R. \bundy}}
\newcommand\bundyname       {\bundyindex\bundynamenoindex}
\newcommand\bundylifetime   {(*1947)}
\newcommand\burris          {{\namefont Burri\es}}
\newcommand\burrisname      {{\namefont\stanley\ \burris}}
\newcommand\burstallindex   {\index{Burstall, Rod M. (*1934)}}
\newcommand\protectedburstallindex{\protect\index{Burstall, Rod M. (*1934)}}
\newcommand\burstall        {{\namefont Burstall}}
\newcommand\burstallname    {\burstallindex{\namefont Rod M. \burstall}}
\newcommand\burstalllifetime{(*1934)}
\newcommand\bush            {Bush}
\newcommand\bushname        {Vannevar \bush}
\newcommand\bussottiindex   {\index{Bussotti, Paolo (*1966)}}
\newcommand\bussotti        {{\namefont Bussotti}}
\newcommand\bussottiname    {\bussottiindex{\namefont\paolo\ \bussotti}}
\newcommand\byrnes          {Byrne\es}
\newcommand\byrnesname      {\john\ \byrnes}
\newcommand\caferra         {{\namefont Caferra}}
\newcommand\caferraname     {{\namefont Ricardo \caferra}}
\newcommand\cantone         {{\namefont Cantone}}
\newcommand\cantonename     {{\namefont Domenico \cantone}}
\newcommand\cantorindex     {\index{Cantor, Georg (1845--1918)}}
\newcommand\protectedcantorindex
                    {\protect\index{Cantor, Georg (1845--1918)}}
\newcommand\cantor          {{\namefont Cantor}}
\newcommand\cantorname      {\cantorindex{\namefont\georg\ \cantor}}
\newcommand\cantorlifetime  {(1845--1918)}
\newcommand\carcavi         {{\namefont Carcavi}}
\newcommand\carcaviname     {{\namefont\pierre\ de \carcavi}}
\newcommand\carnap          {{\namefont Carnap}}
\newcommand\carnapname      {{\namefont\rudolf\ \carnap}}
\newcommand\carnaplifetime  {(1891--1970)}
\newcommand\carroll         {Carroll}
\newcommand\carrollname     {Lewi\es\ \carroll}
\newcommand\carrolltrue     {Dodgson}
\newcommand\carrolltruename {\charles\ Lutwidge \carrolltrue}
\newcommand\carrolllifetime {(1832--1898)}
\newcommand\cassirerindex   {\index{Cassirer, Ernst (1874--1945)}}
\newcommand\cassirer        {{\namefont Cassirer}}
\newcommand\cassirername    {\cassirerindex{\namefont\ernst\ \cassirer}}
\newcommand\cassirerlifetime{(1874--1945)}
\newcommand\cate            {{\namefont Ten Cate}}
\newcommand\catename        {{\namefont Balder \cate}}
\newcommand\cauchyindex     {\index{Cauchy!Augustin Louis}}
\newcommand\cauchy          {{\namefont Cauchy}}
\newcommand\cauchyname      {\cauchyindex{\namefont Augustin Louis \cauchy}}
\newcommand\cauchylifetime  {(1789-1857)}
\newcommand\cavaillesname   {Jean Cavaill\`e\es}
\newcommand\cavailleslifetime{(1903--1944)}
\newcommand\cerrito         {Cerrito}
\newcommand\cerritoname     {Serenella \cerrito}
\newcommand\lassaadsecondname{{\namefont Cheikh\-rou\-hou}}
\newcommand\lassaadname     {{\namefont Las\-saad \lassaadsecondname}}
\newcommand\chrysippos      {{\namefont Chrysippu\es}}
\newcommand\chrysipposname  {{\namefont \chrysippos\ of Soloi} (Asia Minor)}
\newcommand\chrysipposlifetime{(\nth 3\,century\,\BC)}
\newcommand\chrysippossentence{\chrysippos\ sentence}
\newcommand\chevalleyindex  {\index{Chevalley, Claude (1909--1984)}}
\newcommand\protectedchevalleyindex
                            {\protect\index{Chevalley, Claude (1909--1984)}}
\newcommand\chevalley       {{\namefont Chevalley}}
\newcommand\chevalleyname   {\chevalleyindex{\namefont\claude\ \chevalley}}
\newcommand\chevalleylifetime{(1909--1984)}
\newcommand\churchindex     {\index{Church, Alonzo (1903--1995)}}
\newcommand\protectedchurchindex{\protect\index{Church, Alonzo (1903--1995)}}
\newcommand\church          {{\namefont Church}}
\newcommand\churchname      {\churchindex{\namefont Alonzo \church}}
\newcommand\churchlifetime  {(1903--1995)}
\newcommand\churchrosser    {\church--\rosser}
\newcommand\churchrosserproperty{\index
                                {Church--Rosser property}\churchrosser\ property}
\newcommand\churchrossertheorem{\index
                                {Church--Rosser Theorem}\churchrosser\ Theorem}
\newcommand\cialdea         {Cialdea}
\newcommand\cialdeaname     {Marta \cialdea}
\newcommand\clausiusindex   {\index{Clausius, Rudolf (1822--1888)}}
\newcommand\clausius        {{\namefont Clausius}}
\newcommand\clausiusname    {{\namefont\rudolf\ \clausius}}
\newcommand\clausiuslifetime{(1822--1888)}
\newcommand\cleanthes       {Cleanthe\es}
\newcommand\cleanthesname   {\cleanthes\ of Asso\es}
\newcommand\corcoranindex                 {\index{Corcoran, John (*1937)}}
\newcommand\protectedcorcoranindex{\protect\index{Corcoran, John (*1937)}}
\newcommand\corcoran        {{\namefont Corcoran}}
\newcommand\corcoranname    {\corcoranindex{\namefont\john\ \corcoran}}
\newcommand\corcoranlifetime{(*1937)}
\newcommand\comon           {{\namefont Comon}}
\newcommand\comonname       {{\namefont\hubert\ \comon}}
\newcommand\costa           {{\namefont Costa}}
\newcommand\costaname       {{\namefont Newton C. A. da \costa}}
\newcommand\courantindex    {\index{Courant, Richard (1988--1972)}} 
\newcommand\protectedcourantindex
                    {\protect\index{Courant, Richard (1988--1972)}} 
\newcommand\courant         {{\namefont Courant}}
\newcommand\courantname     {\courantindex{\namefont\richard\ \courant}}
\newcommand\courantlifetime {(1988--1972)}
\newcommand\craigindex      {\index{Craig, William (*1918)}}
\newcommand\protectedcraigindex      
                    {\protect\index{Craig, William (*1918)}}
\newcommand\craig           {{\namefont Craig}}
\newcommand\craigname       {\craigindex{\namefont\william\ \craig}}
\newcommand\craiglifetime   {(*1918)}
\newcommand\craigsinterpolationtheorem{\index
                   {Craig's Interpolation Theorem}\craig's Interpolation Theorem}
\newcommand\crelle          {{\namefont Crelle}}
\newcommand\crellename      {{\namefont August \leopold\ \crelle}}
\newcommand\crellelifetime  {(1780--1855)}
\newcommand\crossleyindex                 {\index{Crossley, John N. (*1937)}}
\newcommand\protectedcrossleyindex{\protect\index{Crossley, John N. (*1937)}}
\newcommand\crossley        {{\namefont Crossley}}
\newcommand\crossleyname    {\crossleyindex{\namefont John N. \crossley}}
\newcommand\crossleylifetime{(*1937)}
\newcommand\dalenindex      {\index{Dalen, Dirk van (*1932)}}
\newcommand\protecteddalenindex
                    {\protect\index{Dalen, Dirk van (*1932)}}
\newcommand\dalen           {{\namefont Dalen}}
\newcommand\dalenname       {\dalenindex{\namefont\dirk\ van \dalen}}
\newcommand\dalenlifetime   {(*1932)}
\newcommand\dalton          {Dalton}
\newcommand\daltonname      {\john\ \dalton}
\newcommand\daltonlifetime  {(1766--1844)}
\newcommand\davisindex      {\index{Davis, Martin (*1928)}}
\newcommand\protecteddavisindex
                    {\protect\index{Davis, Martin (*1928)}}
\newcommand\davis           {{\namefont Davis}}
\newcommand\davisname       {\davisindex{\namefont\martin\ \davis}}
\newcommand\davislifetime   {(*1928)}
\newcommand\dawsonindex     {\index{Dawson, John W., \jr\ (*1944)}}
\newcommand\protecteddawsonindex
                    {\protect\index{Dawson, John W., \jr\ (*1944)}}
\newcommand\dawson          {{\namefont Dawson}}
\newcommand\dawsonname      {\dawsonindex{\namefont\john\ W. \dawson\ \jr}}
\newcommand\dawsonlifetime  {(*1944)}
\newcommand\detlefsenindex                 {\index{Detlefsen, Michael (*1948)}}
\newcommand\protecteddetlefsenindex{\protect\index{Detlefsen, Michael (*1948)}}
\newcommand\detlefsen       {{\namefont Detlefsen}}
\newcommand\detlefsenname   
                   {\detlefsenindex{\namefont\michaelwithouttrema\ \detlefsen}}
\newcommand\dieudonneindex  {\index{Dieudonn{\'e}, Jean (1906--1992)}}
\newcommand\protecteddieudonneindex  
                    {\protect\index{Dieudonn{\'e}, Jean (1906--1992)}}
\newcommand\dieudonne       {{\namefont Dieudonn\'e}}
\newcommand\dieudonnename   {\dieudonneindex{\namefont\jean\ \dieudonne}}
\newcommand\dieudonnelifetime{(1906--1992)}
\newcommand\dillerindex     {\index{Diller, Justus}}
\newcommand\diller          {{\namefont Diller}}
\newcommand\dillername      {\dillerindex{\namefont Justu\es\ \diller}}
\newcommand\diophantus      {{\namefont Dio\-phan\-tu\es}}
\newcommand\diophantusname  {{\namefont\diophantus\ of Alexandria}}
\newcommand\diophantuslifetime{(\nth 3\,century?)}
\newcommand\dedekindcutindex{\index{Dedekind cut}}
\newcommand\dedekindcutindexstart{\index{Dedekind cut|(}}
\newcommand\dedekindcutindexstop{\index{Dedekind cut|)}}
\newcommand\dedekindcut     {\dedekindcutindex\dedekind\nolinebreak\ cut}
\newcommand\dedekindindex   {\index{Dedekind, Richard (1831--1916)}}
\newcommand\dedekind        {{\namefont Dedekind}}
\newcommand\dedekindname    {\dedekindindex{\namefont\richard\ \dedekind}}
                           %{J. W. \richard\ \dedekind}
\newcommand\dedekindlifetime{(1831--1916)}
\newcommand\degtyarev       {{\namefont Degtyarev}}
\newcommand\degtyarevname   {{\namefont Anatoli \degtyarev}}
\newcommand\demorgan        {De-Morgan}
\newcommand\demorganname    {Augustus \demorgan}
\newcommand\demorganlifetime{(1806--1871)}
\newcommand\denjoy          {{\namefont Denjoy}}
\newcommand\denjoyname      {{\namefont Arnaud Denjoy}}
\newcommand\denjoylifetime  {(1884--1974)} % verified
\newcommand\denton          {{\namefont Denton}}
\newcommand\dentonname      {{\namefont\john\ \denton}}
\newcommand\deemter          {{\namefont Deemter}}
\newcommand\deemtername      {{\namefont Kees van \deemter}}
\newcommand\dershowitz      {{\namefont Dersho\-witz}}
\newcommand\dershowitzname  {{\namefont Nachum \dershowitz}}
\newcommand\descartes       {{\namefont De\esi carte\es}}
\newcommand\descartesname   {{\namefont\rene\ \descartes}}
\newcommand\descarteslifetime{(1596--1650)}
\newcommand\devidi          {DeVidi}
\newcommand\devidiname      {\david\ \devidi}
\newcommand\dietrich        {{\namefont Diet\-rich}}
\newcommand\dietrichname    {{\namefont Dominik \dietrich}}
\newcommand\dixnoconflict   {Dix}
\newcommand\dixname         {\juergen\ \dixnoconlflict}
\newcommand\dixon           {{\namefont Dixon}}
\newcommand\dixonname       {{\namefont Luca\es\ \dixon}}
\newcommand\doornbos        {Doornbo\es}
\newcommand\doornbosname    {\henk\ \doornbos}
\newcommand\drebenindex                 {\index{Dreben, Burton (1927--1999)}}
\newcommand\protecteddrebenindex{\protect\index{Dreben, Burton (1927--1999)}}
\newcommand\dreben          {{\namefont Dreben}}
\newcommand\drebenname      {\drebenindex{\namefont Burton \dreben}}
\newcommand\drebenlifetime  {(1927--1999)}
\newcommand\dunsscotusindex {\index{Duns-Scotus, Johannes (1265?--1308)}}
\newcommand\dunsscotus      {{\namefont Duns-Scotus}}
\newcommand\dunsscotusname  {\dunsscotusindex{\namefont Johannes \dunsscotus}}
\newcommand\dunsscotuslifetime{(1265?--1308)}
\newcommand\dyckhoffindex   {\index{Dyckhoff, Roy (*1948)}}
\newcommand\dyckhoff        {{\namefont Dyck\-hoff}}
\newcommand\dyckhoffname    {\dyckhoffindex{\namefont Roy \dyckhoff}}
\newcommand\dyckhofflifetime{(*1948)}
\newcommand\ebertindex      {\index{Ebert, Philip}}
\newcommand\ebert           {{\namefont Ebert}}
\newcommand\ebertname       {\ebertindex{\namefont Philip \ebert}}
\newcommand\ebbinghaus      {{\namefont Ebbinghau\es}}
\newcommand\ebbinghauseinsname{{\namefont Heinz-Dieter \ebbinghaus}}
\newcommand\eckmann         {{\namefont Eckmann}}
\newcommand\eckmannname     {{\namefont Beno \eckmann}}
\newcommand\egli            {{\namefont Egli}}
\newcommand\egliname        {{\namefont Ur\es\ \egli}}
\newcommand\egly            {Egly}
\newcommand\eglyname        {\uwe\ \egly}
\newcommand\ehrenfels       {Ehrenfel\es}
\newcommand\ehrenfelsname   {\christian\ von \ehrenfels}
\newcommand\ehrenfelslifetime{(1859--1932)}
\newcommand\ehrig           {{\namefont Ehrig}}
\newcommand\ehrigname       {{\namefont Hartmut \ehrig}}
\newcommand\eijck           {{\namefont Eijck}}
\newcommand\eijckname       {{\namefont \jan\ van \eijck}}
\newcommand\elsenbroichindex{\index{Elsenbroich, Corinna}}
\newcommand\elsenbroich     {{\namefont Elsenbroich}}
\newcommand\elsenbroichname {\elsenbroichindex{\namefont Corinna \elsenbroich}}
\newcommand\einstein        {{\namefont Ein\-stein}}
\newcommand\einsteinname    {{\namefont\albert\ \einstein}}
\newcommand\einsteinlifetime{(1879--1955)}
\newcommand\eisenstein      {{\namefont Eisenstein}}
\newcommand\eisensteinname  {{\namefont Gotthold \eisenstein}}
%                           {\ferdinand\ Gotthold Max \eisenstein}
\newcommand\eisensteinlifetime{(1823--1852)}
\def       \enderton        {{\namefont Enderton}}
%newcommand has problems with \end..
\def       \endertonname    {{\namefont\herbert\ B. \enderton}}
\newcommand\engels          {\mbox{\namefont Engels}}
\newcommand\engelsname      {{\namefont\friedrich\ \engels}}
\newcommand\engesserindex   {\index{Engesser, Kurt}}
\newcommand\engesser        {{\namefont Engesser}}
\newcommand\engessername    {\engesserindex{\namefont\kurt\ \engesser}}
\newcommand\epikurenglish   {{\namefont Epicurius}}
\newcommand\epikurlifetime  {(\ca\,340--\ca\,270\BC)}
\newcommand\epicurean       {{\namefont Epicurean}}
\newcommand\eschbach        {Esch\-bach}
\newcommand\eschbachname    {\robert\ \eschbach}
\newcommand\euclidindex     {\index{Euclid}}
\newcommand\euclid          {{\namefont Euclid}}
\newcommand\euclidlifetime  {(\ca\ 300\,\BC)}
% \newcommand\euclidindex     {\index{Euclid!of Alexandria}}
% \newcommand\euclidname      {\euclidindex{\namefont\euclid\ of Alexandria}}
%Fabio Acerbi: No ancient source assigns Euclid to a town as his birthplace. 
%              Suggestion: skip "of Alexandria"
\newcommand\euclidname      {\euclidindex\euclid}
\newcommand\euklid          {{\namefont Euklid}}
\newcommand\eulerindex      {\index{Euler, Leonhard (1707--1783)}}
\newcommand\euler           {{\namefont Euler}}
\newcommand\eulername       {\eulerindex{\namefont Leon\-hard \euler}}
\newcommand\eulerlifetime   {(1707--1783)}
\newcommand\ewald           {{\namefont Ewald}}
\newcommand\ewaldeinsname   {{\namefont \peter\ \paul\ \ewald}}
\newcommand\ewaldeinslifetime{(1888--1985)}
\newcommand\ewaldzweiname   {{\namefont \william\ \ewald}}
                           %{{\namefont \william\ Bragg \ewald}}
\newcommand\faltings        {{\namefont Faltings}}
\newcommand\faltingsname    {{\namefont \gerd\ \faltings}}
\newcommand\faraday         {Faraday}
\newcommand\fefermanindex   {\index{Feferman, Sol(omon) (*1928)}}
\newcommand\protectedfefermanindex{\protect\index{Feferman, Sol(omon) (*1928)}}
\newcommand\feferman        {{\namefont Fefer\-man}}
\newcommand\fefermanname    {\fefermanindex{\namefont Sol \feferman}}
\newcommand\fefermanlifetime{(*1928)}
\newcommand\fefermanshename {Anita Burdman \feferman}
\newcommand\fenstad         {{\namefont Fenstad}}
\newcommand\fenstadname     {{\namefont Jen\es\ E. \fenstad}}
\newcommand\fermatindex     {\index{Fermat, Pierre (160?--1665)}}
\newcommand\fermat          {\mbox{\namefont Fermat}}
\newcommand\fermatname      {\fermatindex{\namefont \pierre\ \fermat}}
\newcommand\fermatnoblename {\fermatindex{\namefont\pierre\ {\em de} \fermat}}
\newcommand\fermatbirthyear 
% {1607?}
{160?}
\newcommand\fermatdeathyear {1665}
\newcommand\fermatlifetime  {(\fermatbirthyear--\fermatdeathyear)}
\newcommand\letterforhuygensyear{1659}
\newcommand\letterforhuygenstitle
              {Relation des nouvelles d\'ecouvertes en la science des
              nombres}
\newcommand\letterforhuygensproofcitation
                           {\cite[\Vol\,1, \p\,431\f]{fermat-oeuvres}}
\newcommand\fermatsprofession{conseilleur au parlement de Toulouse%
%et commissaire aux requ\^etes
% Das ist nur die Anfaengerposition!!!
}
\newcommand\fermatstitle    {\'eculier}
\newcommand\fermatslasttheorem{\fermat's Last Theorem}
\newcommand\fermatsmother   {{\namefont Claire de Long}}
\newcommand\fermatsstepmother{{\namefont Fran\c coise Cazeneuve}}
\newcommand\fermueller      {{\namefont Fer\-m\ue ller}}
\newcommand\fermuellername  {{\namefont\christian\ G. \fermueller}}
\newcommand\fettig          {Fet\-tig-Vogt}
\newcommand\fettigname      {\roland\ \fettig}
\newcommand\feyerabend      {Feyer\-abend}
\newcommand\feyerabendname  {\paul\ \feyerabend}%{\paul\ K. \feyerabend}
\newcommand\feyerabendlifetime{(1924--1994)}
\newcommand\fichte          {{\namefont Fichte}}
\newcommand\fichtename      {{\namefont \johann\ Gottlieb \fichte}}
\newcommand\fichtelifetime  {(1762--1814)}
\newcommand\fiedler         {{\namefont Fiedler}}
\newcommand\fiedlername     {{\namefont Armin \fiedler}}
\newcommand\fischer         {{\namefont Fischer}}
\newcommand\fischername     {{\namefont\martin\ \fischer}}
% MCMP (Munich Center for Mathematical Philosophy at LMU)
\newcommand\fitting         {{\namefont Fitting}}
\newcommand\fittingname     {{\namefont Melvin       \fitting}}
%                           {{\namefont Melvin C.    \fitting}}
%                           {{\namefont Melvin Ch.   \fitting}}
%                           {{\namefont Melvin Chris \fitting}}
\newcommand\fleuriot        {{\namefont Fleuriot}}
\newcommand\fleuriotname    {{\namefont\jacques\ \fleuriot}}
\newcommand\foellesdal      {{\namefont F\o llesdal}}
\newcommand\foellesdalname  {{\namefont Dagfinn \foellesdal}}
\newcommand\fourcolortheorem{Four-Color Theorem}
\newcommand\fraenkelindex   {\index{Fraenkel, Adolf Abraham (1891--1965)}}
\newcommand\fraenkel        {{\namefont Fraenkel}}
\newcommand\fraenkelname    {\fraenkelindex{\namefont \adolf\ Abraham \fraenkel}}
\newcommand\fraenkellifetime{(1891--1965)}
\newcommand\franke          {{\namefont Franke}}
\newcommand\frankename      {{\namefont\andreas\ \franke}}
\newcommand\fraus           {Frau\es}
\newcommand\frausname       {\ulrich\ \fraus}
\newcommand\frechet         {{\namefont Fr\'echet}}
\newcommand\frechetname     {{\namefont Maurice Ren\'e Fr\'echet}}
\newcommand\frechetlifetime {(1878--1973)} % verified
\newcommand\fregeindex      {\index{Frege, Gottlob (1848--1925)}}
\newcommand\protectedfregeindex{\protect\index{Frege, Gottlob (1848--1925)}}
\newcommand\frege           {{\namefont Frege}}
\newcommand\fregename       {\fregeindex{\namefont \gottlob\ \frege}}
                               %{F. L. \gottlob\ \frege}
\newcommand\fregelifetime   {(1848--1925)} 
\newcommand\Begriffsschrift {Begriff\esi schrift}
\newcommand\frenicle        {{\namefont Fr\'enicle}}
\newcommand\freniclename    {{\namefont\bernard\ \frenicle\ de Bessy}}
\newcommand\freniclelifetime{(1605?--1675)} 
\newcommand\freud           {{\namefont Freud}}
\newcommand\freudname       {{\namefont Sigmund \freud}}
\newcommand\freudlifetime   {(1856--1939)} 
\newcommand\fricke          {{\namefont Fricke}}
\newcommand\frickename      {{\namefont \robert\ \fricke}}
\newcommand\frickelifetime  {(1861--1930)}
\newcommand\friesindex      {\index{Fries, Jakob Friedrich (1773--1843)}}
\newcommand\protectedfriesindex
                            {\protect\index{Fries, Jakob Friedrich (1773--1843)}}
\newcommand\fries           {{\namefont Fries}}
\newcommand\friesname       {\friesindex{\namefont Jakob \friedrich\ \fries}}
\newcommand\frieslifetime   {(1773--1843)} 
\newcommand\furbach         {{\namefont Furbach}}
\newcommand\furbachname     {{\namefont\ulrich\ \furbach}}
\newcommand\furbachlifetime {(*1948)}%\Nov\,16
\newcommand\furtwaengler    {Furt\-w\ae ngler}
\newcommand\furtwaenglername{\wilhelm\ \furtwaengler}
\newcommand\furtwaenglerlifetime{(1886--1954)}
\newcommand\galilei         {{\namefont Gali\-lei}}
\newcommand\galileiname     {{\namefont Gali\-leo \galilei}}
\newcommand\galileilifetime {(1564--1642)}
\newcommand\gaillard        {{\namefont Gaillard}}
\newcommand\gaillardname    {{\namefont \francois\ \gaillard}}
\newcommand\galois          {{\namefont Galoi\es}}
\newcommand\galoisname      {{\namefont Evariste \galois}}
\newcommand\galoislifetime  {(1811--1832)}
\newcommand\gabbayindex     {\index{Gabbay, Dov (*1945)}}
\newcommand\protectedgabbayindex{\protect\index{Gabbay, Dov (*1945)}}
\newcommand\gabbay          {{\namefont Gabbay}}
\newcommand\gabbayname      {\gabbayindex{\namefont Dov \gabbay}}
%                           {{\namefont Dov M. \gabbay}}
\newcommand\gabbaylifetime  {(*1945)}
\newcommand\jamiegabbayindex{\index{Gabbay, Murdoch J.}}
\newcommand\jamiegabbayname {\jamiegabbayindex{\namefont Murdoch J. \gabbay}}
\newcommand\michaelgabbayindex{\index{Gabbay, Michael}}
\newcommand\michaelgabbayname{\michaelgabbayindex{\namefont\michaelwithouttrema\ \gabbay}}
\newcommand\gallier         {Gallier}
\newcommand\galliername     {\jean\ \gallier}
\newcommand\ganzinger       {Gan\-zin\-ger}
\newcommand\ganzingername   {Harald \ganzinger}
\newcommand\gauss           {{\namefont Gau\sz}}
\newcommand\gaussname       {{\namefont\carl\ \friedrich\ \gauss}}
\newcommand\gausslifetime   {(1777--1855)}
\newcommand\gentzenindex    {\index{Gentzen, Gerhard (1909--1945)}}
\newcommand\gentzen         {{\namefont Gentzen}}
\newcommand\gentzenname     {\gentzenindex{\namefont\gerhard\ \gentzen}}
\newcommand\gentzenlifetime {(1909--1945)}
\newcommand\gentzensHauptsatz{{\namefont\gentzen}'\es\ {\Hauptsatz}}
\newcommand\gentzensverschaerfterHauptsatz
{{\namefont\gentzen}'\es\ {\germanfont\verschaerfterHauptsatz}}
\newcommand\gentzensverschaerfterHauptsatzfootnote
{{\namefont\gentzen}'\es\ {\germanfontfootnote\verschaerfterHauptsatz}}
\newcommand\verschaerfterHauptsatz{Ver\-sch\ae rf\-ter \Hauptsatz}
\newcommand\Hauptsatz{Haupt\-satz}
\newcommand\gerickeindex    {\index{Gericke, Otto (von Guericke) (1602--1686)}}
\newcommand\gericke         {{\namefont Gericke}}
\newcommand\gerickename     {\gerickeindex{\namefont Otto \gericke}}
\newcommand\gerickelifetime {(1602--1686)}
\newcommand\gersonindex     {\index{Gerson, Levi ben (1288--1344)}}
\newcommand\gerson          {{\namefont Gerson}}
\newcommand\gersonname      {\gersonindex{\namefont Levi ben \gerson}}
\newcommand\gersonlifetime  {(1288--1344)}
\newcommand\geurts          {Geurt\es}
\newcommand\geurtsname      {Bart \geurts}
\newcommand\geserindex      {\index{Geser, Alfons}}
\newcommand\geser           {Geser}
\newcommand\gesername       {Alfons \geser}
% \newcommand\geserlifetime   {(*19??)}
\newcommand\giese           {{\namefont Giese}}
\newcommand\giesename       {{\namefont\martin\ \giese}}
\newcommand\giesl           {Giesl}
\newcommand\gieslname       {\juergen\ \giesl}
\newcommand\gilmoreindex    {\index{Gilmore, Paul C. (*1925)}}
\newcommand\gilmore         {{\namefont Gilmore}}
\newcommand\gilmorename     {\gilmoreindex{\namefont\paul\ C. \gilmore}}
\newcommand\gilmorelifetime {(*1925)}
\newcommand\goedelindex     {\index{Goedel, Kurt@G\"odel, Kurt (1906--1978)}}
\newcommand\protectedgoedelindex
                    {\protect\index{Goedel, Kurt@G\"odel, Kurt (1906--1978)}}
\newcommand\goedelindexbegin{\index{Goedel, Kurt@G\"odel, Kurt (1906--1978)}}
\newcommand\goedelindexend  {\index{Goedel, Kurt@G\"odel, Kurt (1906--1978)}}
\newcommand\goedel          {{\namefont G\oe del}}
\newcommand\goedelname      {\goedelindex{\namefont \kurt\ \goedel}}
\newcommand\goedellifetime  {(1906--1978)}
\newcommand\goedelssecondincompletenesstheorem
{\goedel'\es\ \secondincompletenesstheorem}
\newcommand\goedelssecondIncompletenessTheorem
{\goedel'\es\ \secondIncompletenessTheorem}
\newcommand\secondincompletenesstheorem
% {\nth 2 \incompletenesstheorem}
{second \incompletenesstheorem}
\newcommand\secondIncompletenessTheorem
% {\nth 2 \IncompletenessTheorem}
{Second \IncompletenessTheorem}
\newcommand\goedelsfirstincompletenesstheorem
{\goedel'\es\ \firstincompletenesstheorem}
\newcommand\goedelsfirstIncompletenessTheorem
{\goedel'\es\ \firstIncompletenessTheorem}
\newcommand\firstincompletenesstheorem
% {\nth 2 \incompletenesstheorem}
{first \incompletenesstheorem}
\newcommand\firstIncompletenessTheorem
% {\nth 2 \IncompletenessTheorem}
{First \IncompletenessTheorem}
\newcommand\incompletenesstheorem{incompleteness theorem}
\newcommand\IncompletenessTheorem{Incompleteness Theorem}
\newcommand\goethe          {{\namefont G\oe the}}
\newcommand\goethename      {{\namefont \johann\ \wolfgang\ von \goethe}}
\newcommand\gogolla         {Gogolla}
\newcommand\gogollaname     {\martin\ \gogolla}
\newcommand\goguen          {{\namefont Goguen}}
\newcommand\goguenname      {{\namefont\joseph\ \goguen}}
\newcommand\goldbachindex   {\index{Goldbach, Christian (1690--1764)}}
\newcommand\goldbach        {{\namefont Gold\-bach}}
\newcommand\goldbachname    {\goldbachindex{\namefont\christian\ \goldbach}}
\newcommand\goldbachlifetime{(1690--1764)}
\newcommand\goldbachsconjecture
                           {\index{Goldbach's Conjecture}\goldbach's Conjecture}
\newcommand\goldfarbindex   {\index{Goldfarb, Warren}}
\newcommand\protectedgoldfarbindex{\protect\index{Goldfarb, Warren}}
\newcommand\goldfarb        {{\namefont Gold\-farb}}
\newcommand\goldfarbname    {\goldfarbindex{\namefont\warren\ %D.
                              \goldfarb}}
\newcommand\goldsteinindex  {\index{Goldstein, Catherine (*1958)}}
\newcommand\protectedgoldsteinindex{\protect\index{Goldstein, Catherine (*1958)}}
\newcommand\goldstein       {{\namefont Gold\-stein}}
\newcommand\goldsteinname   {\goldsteinindex{\namefont\catherine\ \goldstein}}
\newcommand\goldsteinlifetime{(*1958)}
\newcommand\gonseth         {{\namefont Gonseth}}
\newcommand\gonsethname     {{\namefont \ferdinand\ \gonseth}}
\newcommand\gordonindex     {\index{Gordon, Mike J. C. (*1948)}}
\newcommand\protectedgordonindex{\protect\index{Gordon, Mike J. C. (*1948)}}
\newcommand\gordon          {{\namefont Gordon}}
\newcommand\gordonname      {\gordonindex{\namefont Mike J. C. \gordon}}
\newcommand\gordonlifetime  {(*1948)}
\newcommand\gow             {{\namefont Gow}}
\newcommand\gowname         {{\namefont Jeremy \gow}}
\newcommand\gramlichindex           {\index{Gramlich, Bernhard (1959--2014)}}
\newcommand\protectedgramlichindex
                            {\protect\index{Gramlich, Bernhard (1959--2014)}}
\newcommand\gramlich        {{\namefont Gram\-lich}}
\newcommand\gramlichnamenoindex{{\namefont\bernhard\ \gramlich}}
\newcommand\gramlichname    {\gramlichindex\gramlichnamenoindex}
\newcommand\gramlichlifetime{(1959--2014)}
\newcommand\greensurname    {{\namefont Green}}
\newcommand\greenname       {{\namefont Ian \greensurname}}
\newcommand\grimm           {Grimm}
\newcommand\grimmjacobname  {Jacob \grimm}
\newcommand\grimmwilhelmname{\wilhelm\ \grimm}
\newcommand\grothendieck    {{\namefont Grothendieck}}
\newcommand\grothendieckname{{\namefont\alexander\ \grothendieck}}
\newcommand\grothendiecklifetime{(*1928)}
\newcommand\guillaume       {{\namefont Guillaume}}
\newcommand\guillaumename   {{\namefont Marcel \guillaume}}
\newcommand\gurevich        {{\namefont Gurevich}}
\newcommand\gurevichname    {{\namefont Yuri \gurevich}}
% H %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand\hadamard        {{\namefont Hadamard}}
\newcommand\hadamardname    {{\namefont\jacques\ Salomon \hadamard}}
\newcommand\hadamardlifetime{(1865--1963)}
\newcommand\haehnle         {{\namefont H\ae hnle}}
\newcommand\haehnlename     {{\namefont Reiner \haehnle}}
\newcommand\haerdername     {Theo H\ae r\-der}
\newcommand\hahn            {{\namefont Hahn}}
\newcommand\hahnname        {{\namefont\ottonoconflict\ \hahn}}
\newcommand\hahnlifetime    {(1879--1968)}
\newcommand\hailperin       {{\namefont Hailperin}}
\newcommand\hailperinname   {{\namefont Theodore \hailperin}}
\newcommand\hallett         {{\namefont Hallett}}
\newcommand\hallettname     {{\namefont\michaelwithouttrema\ \hallett}}
\newcommand\hallmann        {{\namefont Hall\-mann}}
\newcommand\hallmannname    {{\namefont\andreas\ \hallmann}}
\newcommand\hamilton        {{\namefont Hamilton}}
\newcommand\hamiltonname    {{\namefont Geoff \hamilton}}
\newcommand\hamoen          {Hamoen}
\newcommand\hamoenname      {Erik \hamoen}
\newcommand\hanus           {Hanu\es}
\newcommand\hanusname       {\michaelwithouttrema\ \hanus}
\newcommand\harmelenindex   {\index{Harmelen, Frank van (*1960)}}
\newcommand\protectedharmelenindex{\protect\index{Harmelen, Frank van (*1960)}}
\newcommand\harmelen        {{\namefont Harmelen}}
\newcommand\harmelenname    {\harmelenindex{\namefont\frank\ van \harmelen}}
\newcommand\harmelenlifetime{(*1960)}
\newcommand\hartogs         {{\namefont Hartogs}}
\newcommand\hartogsname     {{\namefont\friedrich\ \hartogs}}
\newcommand\hartogslifetime {(1874--1943)}
\newcommand\hartogswellorderingtheorem{\hartogs' Ordinal Theorem}
\newcommand\hasenjaegerindex{\index{Hasenjaeger, Gisbert (1919--2006)}}
\newcommand\hasenjaeger     {{\namefont Hasenjaeger}}
\newcommand\hasenjaegername {\hasenjaegerindex{\namefont Gisbert \hasenjaeger}}
\newcommand\hasenjaegerlifetime{(1919--2006)}
\newcommand\hasseindex      {\index{Hasse, Helmut (1898--1979)}}
\newcommand\protectedhasseindex
                    {\protect\index{Hasse, Helmut (1898--1979)}}
\newcommand\hasse           {{\namefont Hasse}}
\newcommand\hassename       {\hasseindex{\namefont\helmut\ \hasse}}
\newcommand\hasselifetime   {(1898--1979)}
\newcommand\haubrich        {{\namefont Haubrich}}
\newcommand\haubrichname    {{\namefont Ralf \haubrich}}
\newcommand\hauff           {{\namefont Hauff}}
\newcommand\hauffname       {{\namefont\wilhelm\ \hauff}}
\newcommand\haufflifetime   {(1802--1827)}
\newcommand\hayesindex      {\index{Hayes, Pat(rick) J. (*1944)}}
\newcommand\protectedhayesindex{\protect\index{Hayes, Pat(rick) J. (*1944)}}
\newcommand\hayes           {{\namefont Hayes}}
\newcommand\hayesname       {\hayesindex{\namefont Pat \hayes}}
\newcommand\hayeslifetime   {(*1944)}
% He
\newcommand\heath           {{\namefont Heath}}
\newcommand\heathname       {{\namefont \thomas\ L. \heath}}
\newcommand\heathlifetime   {(1861--1940)}
\newcommand\hecke           {{\namefont Hecke}}
\newcommand\heering         {Heering}
\newcommand\heeringname     {\jan\ \heering}
% Heg
\newcommand\hegel           {{\namefont Hegel}}
\newcommand\hegelname       {{\namefont\georg\ \friedrich\ \hegel}}
\newcommand\hegellifetime   {(1770--1831)}
% Hei
\newcommand\heideggerindex  {\index{Heidegger, Martin (1889--1976)}}
\newcommand\heidegger       {\mbox{\namefont Heidegger}}
\newcommand\heideggername   {\heideggerindex{\namefont\martin\ \heidegger}}
\newcommand\heideggerlifetime{(1889--1976)}
\newcommand\heijenoortindex {\index{Heijenoort, Jean van (1912--1986)}}
\newcommand\protectedheijenoortindex
                            {\protect\index{Heijenoort, Jean van (1912--1986)}}
\newcommand\heijenoort      {{\namefont Heijen\-oort}}
\newcommand\vanheijenoort   {{\namefont van Heijen\-oort}}
\newcommand\heijenoortname  {\heijenoortindex{\namefont\jean\ %L. M. 
                             \vanheijenoort}}
\newcommand\heijenoortdeathyear{1986}
\newcommand\heijenoortlifetime{(1912--\heijenoortdeathyear)}
\newcommand\heijenoortonherbrandunpublishedtitle
{On the relation between the Falsifiability Tree Method and the 
\herbrand\ Method in Quantification Theory}
\newcommand\heisenberg      {{\namefont Heisen\-berg}}
\newcommand\heisenbergname  {{\namefont\werner\ \heisenberg}}
\newcommand\heisenberglifetime{(1901--1976)}
% Hel
\newcommand\helmholtzindex  {\index{Helmholtz, Hermann von (1821--1894)}}
\newcommand\helmholtz       {{\namefont Helm\-holtz}}
\newcommand\helmholtzname   {\helmholtzindex{\namefont \hermann\ von \helmholtz}}
\newcommand\helmholtzlifetime{(1821--1894)}
% Hen
\newcommand\hendricksindex  {\index{Hendricks, Vincent F. (*1970)}}
\newcommand\hendricks       {{\namefont Hendrick\es}}
\newcommand\hendricksname   {\hendricksindex{\namefont Vincent F. \hendricks}}
\newcommand\hendrickslifetime{(*1970)}
\newcommand\henkin          {{\namefont Henkin}}
\newcommand\henkinname      {{\namefont \leon\ \henkin}}
\newcommand\henkinlifetime  {(1921--2006)}
\newcommand\henryname       {{\namefont\charles\ \henry}}
\newcommand\henrylifetime   {(1859--1926)}
% Her
\newcommand\herbrandindex     {\index{Herbrand, Jacques (1908--1938)}}
\newcommand\protectedherbrandindex
                      {\protect\index{Herbrand, Jacques (1908--1938)}}
\newcommand\herbrandindexbegin{\index{Herbrand, Jacques (1908--1938)|(}}
\newcommand\herbrandindexend  {\index{Herbrand, Jacques (1908--1938)|)}}
\newcommand\herbrand        {{\namefont Herbrand}}
\newcommand\herbrandname    {\herbrandindex{\namefont \jacques\ \herbrand}}
\newcommand\herbranddeathyear{1931}
\newcommand\herbrandlifetime{(1908--\herbranddeathyear)}
\newcommand\herbrandbirthday{\Feb\,12, 1908}
\newcommand\herbranddeathday{\Jul\,27, \herbranddeathyear}
\newcommand\herbrandPhDtitle
{Recherche\es\ sur la th\'eorie de la d\'e\-mon\-stra\-tion}
\newcommand\herbrandPhDdefensedate{\Jun\,11, 1930}
\newcommand\herbrandPhDapprovedforpublicationdate{\Jun\,20, 1929}
\newcommand\herbrandPhDdating{\Apr\,14, 1929}
\newcommand\herbrandtogoedeldate{\Apr\,7, 1931}
\newcommand\herbrandsfundamentaltheoremindex
                                       {\index{Herbrand's Fundamental Theorem}}
\newcommand\herbrandsfundamentaltheoremindexbegin
                                       {\index{Herbrand's Fundamental Theorem|(}}
\newcommand\herbrandsfundamentaltheoremindexend
                                       {\index{Herbrand's Fundamental Theorem|)}}
\newcommand\herbrandsfundamentaltheoremnoindex
                                             {\herbrand'\es\ \fundamentaltheorem}
\newcommand\herbrandsfundamentaltheorem
           {\herbrandsfundamentaltheoremindex\herbrandsfundamentaltheoremnoindex}
\newcommand\herbrandsfalselemmaindex{\index{Herbrand's ``False Lemma''}}
\newcommand\herbrandsfalselemma
                           {\herbrandsfalselemmaindex\herbrand's ``False Lemma''}
\newcommand\herbrandsfalselemmacomma
             {\herbrandsfalselemmaindex\herbrand's ``False Lemma\closequotecomma}
\newcommand\herbrandsfalselemmafullstop
          {\herbrandsfalselemmaindex\herbrand's ``False Lemma\closequotefullstop}
\newcommand\herbrandsfalselemmawithinquotedtext
                           {\herbrandsfalselemmaindex\herbrand's `False Lemma'}
\newcommand\herbrandsfalselemmawithoutherbrand
                           {\herbrandsfalselemmaindex``False Lemma''}
\newcommand\herbrandsfalselemmawithoutherbrandcomma
                         {\herbrandsfalselemmaindex``False Lemma\closequotecomma}
\newcommand\fundamentaltheorem{Fundamental Theorem}
\newcommand\textonherbrandlogicalwritings{%
 This edition is still an excellent source on \herbrand's writings today,
 but it is problematic because 
 it is based on the contorted reprint \cite{herbrand-ecrits-logiques}. 
 \hskip.3em
 This means that it urgently needs a corrected edition based on 
 the original editions of\/ \herbrand's logical writings,
 which are all in French and which should be included 
 in facsimile to avoid future contortion.}
\newcommand\herbrandsfatherindex{\index
                                 {Herbrand, Jacques, \sr\ (Herbrand's father)}}
\newcommand\protectedherbrandsfatherindex{\protect\index
                                 {Herbrand, Jacques, \sr\ (Herbrand's father)}}
\newcommand\herbrandsfatherindexbegin{\index
                                 {Herbrand, Jacques, \sr\ (Herbrand's father)|(}}
\newcommand\herbrandsfatherindexend{\index
                                 {Herbrand, Jacques, \sr\ (Herbrand's father)|)}}
\newcommand\herbrandsfathername
                      {\herbrandsfatherindex{\namefont\jacques\ \herbrand\ \sr}}
\newcommand\herbrandribet   {\herbrand--\ribet}
\newcommand\herder          {{\namefont Herder}}
\newcommand\herdername      {{\namefont\johann\ \gottfried\ \herder}}
\newcommand\herderlifetime  {(1744--1803)}
\newcommand\hermes          {{\namefont Herme\es}}
\newcommand\hermesname      {{\namefont\hans\ \hermes}}
\newcommand\hertz           {{\namefont Hertz}}
\newcommand\hertzeinsindex  {\index{Hertz, Heinrich (1857--1894)}}
\newcommand\hertzeinsname   {\hertzeinsindex{\namefont\heinrich\ \hertz}}
\newcommand\hertzeinslifetime{(1857--1894)}
\newcommand\hertzzweiname   {{\namefont\gustav\ \hertz}}
\newcommand\hertzzweilifetime{(1887--1975)}
\newcommand\hertzdreiphysicistindex {\index{Hertz, Paul (1881--1940)}}
\newcommand\protectedhertzdreiphysicistindex
                            {\protect\index{Hertz, Paul (1881--1940)}}
\newcommand\hertzdreiphysicistname
                            {\hertzdreiphysicistindex{\namefont\paul\ \hertz}}
\newcommand\hertzdreiphysicistlifetime{(1881--1940)}
\newcommand\hertzdreipoliticianname{{\namefont\paul\ \hertz}}
\newcommand\hertzdreipoliticianlifetime{(1888--1961)}
% Hes
\newcommand\hessenbergindex {\index{Hessenberg, Gerhard (1847--1925)}}
\newcommand\hessenberg      {{\namefont Hessenberg}}
\newcommand\hessenbergname  {\hessenbergindex{\namefont Gerhard \hessenberg}}
\newcommand\hessenberglifetime{(1847--1925)}
% Heu
\newcommand\heusinger       {Heusinger}
\newcommand\heusingername   {\klaus\ von \heusinger}
\newcommand\heytingindex                 {\index{Heyting, Arend (1898--1980)}}
\newcommand\protectedheytingindex{\protect\index{Heyting, Arend (1898--1980)}}
\newcommand\heytingindexbegin            {\index{Heyting, Arend (1898--1980)|(}}
\newcommand\heytingindexend              {\index{Heyting, Arend (1898--1980)|)}}
\newcommand\heyting         {\mbox{\namefont Heyting}}
\newcommand\heytingname     {\heytingindex{\namefont Arend \heyting}}
\newcommand\heytinglifetime {(1898--1980)}
% Hi
\newcommand\hilbertindex                 {\index{Hilbert, David (1862--1943)}}
\newcommand\protectedhilbertindex{\protect\index{Hilbert, David (1862--1943)}}
\newcommand\hilbertindexbegin            {\index{Hilbert, David (1862--1943)|(}}
\newcommand\hilbertindexend              {\index{Hilbert, David (1862--1943)|)}}
\newcommand\hilbert         {\mbox{\namefont Hilbert}}
\newcommand\hilbertname     {\hilbertindex{\namefont \david\ \hilbert}}
\newcommand\hilbertlifetime {(1862--1943)}
\newcommand\hilbertsprogram {\hilbert'\es\ \programme}
\newcommand\hilbertsProgram {\hilbert'\es\ \Programme}
\newcommand\hilbertsprogramgerman{\hilbert\es\ Programm}
\newcommand\hilbertsepsilonlongindex{\index{Hilbert!'s epsilon}}
\newcommand\hilbertsepsilonlong{\hilbertsepsilonlongindex\hilbert'\es\ epsilon}
\newcommand\hilbertsepsilon
                     {\hilbertsepsilonlongindex\hilbert'\es\ \nlbmath\varepsilon}
\newcommand\hilbertbernays  {\hilbert--\bernays}
\newcommand\hilbertbernaysprojectgerman{{\namefont\hilbertbernays-Pro\-jekt}}
\newcommand\hilbertbernaysproject{{\namefont\hilbertbernays\ Pro\-ject}}
\newcommand\whatisinVolIPartA
                       {Title Pages, Prefaces, and \mbox{\litsectfromtoref 1 2}}
\newcommand\whatisinVolIPartB
                 {\litsectfromtoref 3 5 and Deleted Part\,I of the \nth 1\,\Edn}
\newcommand\ISBNVolIPartA   {ISBN\,\,978--1--84890--033--2}
\newcommand\ISBNVolIPartB   {ISBN\,\,978--1--84890--075--2}
\newcommand\hillenbrandindex{\index{Hillenbrand, Thomas}}
\newcommand\protectedhillenbrandindex{\protect\index{Hillenbrand, Thomas}}
\newcommand\hillenbrand     {{\namefont Hillenbrand}}
\newcommand\hillenbrandname {\hillenbrandindex{\namefont\thomas\ \hillenbrand}}
\newcommand\hintermeier     {Hinter\-meier}
\newcommand\hintermeiername {\claus\ \hintermeier}
\newcommand\hintikka        {{\namefont Hintikka}}
\newcommand\hintikkaname    {{\namefont Jaakko \hintikka}}
%                           {K. Jaakko J. \hintikka}
\newcommand\hippasosindex   {\index{Hippasus of Metapontum (\ca\,550\,\BC)}}
\newcommand\hippasos        {{\namefont Hippasu\es}}
\newcommand\hippasosname    {\hippasosindex{\namefont\hippasos\ of Metapontum}}
\newcommand\hippasoslifetime{(\ca\,550\,\BC)}
\newcommand\hippasosgerman  {{\namefont Hippaso\es}}
\newcommand\hippasosnamegerman{{\namefont\hippasosgerman\ von Metapont}}
\newcommand\hoare           {Hoare}
\newcommand\hoarename       {C. A. R. \hoare}
\newcommand\hobbes          {{\namefont Hobbe\es}}
\newcommand\hobbesname      {{\namefont\thomas\ \hobbes}}
\newcommand\hobbeslifetime  {(1588--1679)}
\newcommand\hobbs           {{\namefont Hobb\es}}
\newcommand\hobbsname       {{\namefont Jerry R. \hobbs}}
\newcommand\hoeven          {Hoeven}
\newcommand\hoevenname      {Jori\es\ van der \hoeven}
\newcommand\hogger          {{\namefont Hogger}}
\newcommand\hoggername      {{\namefont Christopher \john\ \hogger}}
\newcommand\honneth         {{\namefont Honneth}}
\newcommand\honnethname     {{\namefont Axel \honneth}}
\newcommand\honnethlifetime {(*1949)}
\newcommand\horacek         {{\namefont Horacek}}
\newcommand\horacekname     {{\namefont\helmut\ \horacek}}
\newcommand\hornindex       {\index{Horn, Alfred (1918--2001)}}
\newcommand\horn            {{\namefont Horn}}
\newcommand\hornname        {\hornindex{\namefont\alfred\ \horn}}
\newcommand\hornlifetime    {(1918--2001)}
\newcommand\hornclauselogic {\horn-clause logic}
% Paul Howard:  Aug. 31, 1943 -- info by Paul Howard
\newcommand\howardindex                 {\index{Howard, Paul (*1943)}}
\newcommand\protectedhowardindex{\protect\index{Howard, Paul (*1943)}}
\newcommand\howardname      {{\namefont\paul\ \howard}}
\newcommand\huebner         {H\ue bner}
\newcommand\huebnername     {Malte \huebner}
\newcommand\hudlak          {Hudlak}
\newcommand\hudlakname      {\paul\ \hudlak}
\newcommand\huet            {Huet}
\newcommand\huetname        {G\'erard \huet}
\newcommand\huff            {{\namefont Huff}}
\newcommand\huffname        {{\namefont\george\ \huff}}
\newcommand\hullot          {Hullot}
\newcommand\hullotname      {\jean-Marie \hullot}
\newcommand\humboldt        {{\namefont Hum\-boldt}}
\newcommand\humboldtname    {{\namefont \alexander\ von \humboldt}}
\newcommand\humboldtlifetime{(1769--1859)}
\newcommand\hume            {{\namefont Hume}}
\newcommand\humename        {{\namefont \david\ \hume}}
\newcommand\humelifetime    {(1711--1776)}
\newcommand\huntindex       {\index{Hunt, Warren A.}}
\newcommand\protectedhuntindex{\protect\index{Hunt, Warren A.}}
\newcommand\hunt            {{\namefont Hunt}}
\newcommand\huntname        {\huntindex{\namefont\warren~A. \hunt}}
% \newcommand\huntlifetime    {(*)}
\newcommand\huntingtonindex {\index{Huntington, Edward V. (1874--1952)}}
\newcommand\huntington      {{\namefont Huntington}}
\newcommand\huntingtonname  {\huntingtonindex{\namefont\edward\ V. \huntington}}
\newcommand\huntingtonlifetime{(1874--1952)}
\newcommand\hurwitzindex    {\index{Hurwitz, Adolf (1859--1919)}}
\newcommand\hurwitz         {{\namefont Hurwitz}}
\newcommand\hurwitzname     {\hurwitzindex{\namefont\adolf\ \hurwitz}}
\newcommand\hurwitzlifetime {(1859--1919)}
\newcommand\husserlindex    {\index{Husserl, Edmund (1859--1938)}}
\newcommand\husserl         {{\namefont Husserl}}
\newcommand\husserlname     {\husserlindex{\namefont\edmund\ \husserl}}
\newcommand\husserllifetime {(1859--1938)}
\newcommand\hutterindex     {\index{Hutter, Dieter (*1959)}}
\newcommand\protectedhutterindex{\protect\index{Hutter, Dieter (*1959)}}
\newcommand\hutter          {{\namefont Hutter}}
\newcommand\huttername      {\hutterindex{\namefont\dieter\ \hutter}}
\newcommand\hutterlifetime  {(*1959)}
\newcommand\huygensindex    {\index{Huygens, Christiaan (1629--1695)}}
\newcommand\huygens         {{\namefont Huygen\es}}
\newcommand\huygensname     {\huygensindex{\namefont Christiaan \huygens}}
\newcommand\huygenslifetime {(1629--1695)}
\newcommand\irelandindex    {\index{Ireland, Andrew}}
\newcommand\protectedirelandindex{\protect\index{Ireland, Andrew}}
\newcommand\ireland         {{\namefont Ireland}}
\newcommand\irelandname     {\irelandindex{\namefont\andrew\ \ireland}}
\newcommand\jaescheindex    {\index{Jaesche, Gottlob Benjamin (1762--1842)@J\ae sche, Gottlob Benjamin (1762--1842)}}
\newcommand\jaesche         {{\namefont J\ae sche}}
\newcommand\jaeschename {\jaescheindex{\namefont\gottlob\ \benjamin\ J\ae sche}}
\newcommand\jaskowskiindex
                      {\index{Jaskowski@Ja{\'s}kowski, \stanislaw\ (1906--1965)}}
\newcommand\jaskowski       {\mbox{\namefont Ja{\'s}kowski}}
\newcommand\jaskowskiname   {\jaskowskiindex{\namefont \stanislaw\ \jaskowski}}
\newcommand\jaskowskilifetime{(1906--1965)}
\newcommand\jaspersindex    {\index{Jaspers, Karl (1883--1969)}}
\newcommand\jaspers         {{\namefont Jasper\es}}
\newcommand\jaspersname     {\jaspersindex{\namefont\karl\ \jaspers}}
\newcommand\jasperslifetime {(1883--1969)}
\newcommand\jevonsindex     {\index{Jevons, William Stanley (1835--1882)}}
\newcommand\jevons          {{\namefont Jevons}}
\newcommand\jevonsname      {\jevonsindex{\namefont \william\ \stanley\ \jevons}}
\newcommand\jevonslifetime  {(1835--1882)}
\newcommand\jouannaud       {Jouannaud}
\newcommand\jouannaudname   {\jean-\pierre\ \jouannaud}
\newcommand\kahle           {{\namefont Kahle}}
\newcommand\kahlename       {{\namefont Rein\-hard \kahle}}
\newcommand\kalmarindex     {\index{Kalmar@Kalm\'ar, L\'aszl\'o (1905--1976)}}
\newcommand\kalmar          {{\namefont Kalm\'ar}}
\newcommand\kalmarname      {\kalmarindex{\namefont L\'aszl\'o \kalmar}}
\newcommand\kalmarlifetime  {(1905--1976)}
\newcommand\kamp            {Kamp}
\newcommand\kampname        {\hans\ \kamp}
\newcommand\kanger          {Kan\-ger}
\newcommand\kangername      {Stig \kanger}
\newcommand\kantindex                 {\index{Kant, Immanuel (1724--1804)}}
\newcommand\protectedkantindex{\protect\index{Kant, Immanuel (1724--1804)}}
\newcommand\kantindexbegin            {\index{Kant, Immanuel (1724--1804)|(}}
\newcommand\kantindexend              {\index{Kant, Immanuel (1724--1804)|)}}
\newcommand\kant            {{\namefont Kant}}
\newcommand\kantname        {\kantindex{\namefont\immanuelwithouttrema\ \kant}}
\newcommand\kantdeathyear   {1804}
\newcommand\kantlifetime    {(1724--\kantdeathyear)}
\newcommand\kaplan          {Kaplan}
\newcommand\kaplanname      {St\'ephane \kaplan}
\newcommand\kapur           {Kapur}
\newcommand\kapurname       {Deepak \kapur}
\newcommand\kaufmannindex   {\index{Kaufmann, Matt (*1952)}}
\newcommand\protectedkaufmannindex{\protect\index{Kaufmann, Matt (*1952)}}
\newcommand\kaufmann        {{\namefont Kaufmann}}
\newcommand\kaufmannname    {\kaufmannindex{\namefont Matt \kaufmann}}
\newcommand\kaufmannlifetime{(*1952)}
\newcommand\kelley          {{\namefont Kelley}}
\newcommand\kelleyname      {{\namefont \john\ L. \kelley}}
\newcommand\kelleylifetime  {(1916--1999)}
\newcommand\kepler          {{\namefont Kepler}}
\newcommand\keplername      {{\namefont Johanne\es\ \kepler}}
\newcommand\keplerlifetime  {(1571--1630)}
\newcommand\kerber          {Kerber}
\newcommand\kerbername      {\manfred\ \kerber}
\newcommand\kernighan       {Kernighan}
\newcommand\kernighanname   {Brian W. \kernighan}
\newcommand\keynesindex     {\index{Keynes, John Maynard (1883--1946)}}
\newcommand\keynes          {{\namefont Keynes}}
\newcommand\keynesname      {\keynesindex{\namefont \john\ Maynard \keynes}}
\newcommand\keyneslifetime  {(1883--1946)}
\newcommand\kleeneindex     {\index{Kleene, Stephen C. (1909--1994)}}
\newcommand\kleene          {{\namefont Kleene}}
\newcommand\kleenename      {\kleeneindex{\namefont Stephen C. \kleene}}
%                            {Stephen Cole \kleene}
\newcommand\kleenelifetime  {(1909--1994)}
\newcommand\klint           {Klint}
\newcommand\klintname       {\paul\ \klint}
\newcommand\klop            {Klop}
\newcommand\klopname        {\jan\ Willem \klop}
\newcommand\knuth           {{\namefont Knuth}}
\newcommand\knuthname       {{\namefont\donald\ E. \knuth}}
\newcommand\koenig          {{\namefont K\oe nig}}
% This should actually be:  {{\namefont K\H onig}}, but Julius did not use it
%                           in his pubications, and Denes is less important,
%                           in spite of providing Koenig's Lemma.
\newcommand\koenigname      {{\namefont D\'enes \koenig}}
\newcommand\koenigfathername{{\namefont\julius\ \koenig}}
\newcommand\koenigslemmaindex{\index
                             {choice!Koenig's Lemma@K{\"o}nig's Lemma}}
\newcommand\koenigslemmaindexbegin{\index
                             {choice!Koenig's Lemma@K{\"o}nig's Lemma|(}}
\newcommand\koenigslemmaindexend{\index
                             {choice!Koenig's Lemma@K{\"o}nig's Lemma|)}}
\newcommand\koenigslemmaindexsee{\index
              {Koenig's Lemma@K{\"o}nig's Lemma|see{choice, K{\"o}nig's Lemma}}}
\newcommand\koenigslemma    {\koenigslemmaindex\koenig's Lemma}
\newcommand\kohlhase        {{\namefont Kohl\-hase}}
\newcommand\kohlhasename    {{\namefont\michaelwithouttrema\ \kohlhase}}
\newcommand\koller          {Koller}
\newcommand\kollername      {\alexander\ \koller}
\newcommand\kolmogorovindex {\index{Kolmogorov, Andrey (1903--1987)}}
\newcommand\kolmogorov      {{\namefont Kolmogorov}}
\newcommand\kolmogorovname  {\kolmogorovindex{\namefont Andrey \kolmogorov}}
\newcommand\kolmogorovlifetime{(1903--1987)}
\newcommand\kopernik        {Koper\-nik}% Das ist der einzige korrekte 
                                     % original polnische Name!
\newcommand\kopernikname    {Niko\-lau\es\ \kopernik}
\newcommand\koperniklifetime{(1473--1543)}
\newcommand\kopernikan      {\kopernik an}
\newcommand\kopernikanisch  {\kopernik a\-nisch}
\newcommand\kounalis        {{\namefont Kounali\es}}
\newcommand\kounalisname    {{\namefont Emmanu\ewithtrema l \kounalis}}
\newcommand\kowalskiindex   {\index{Kowalski, Robert A. (*1941)}}
\newcommand\protectedkowalskiindex{\protect\index{Kowalski, Robert A. (*1941)}}
\newcommand\kowalski        {{\namefont Kowalski}}
\newcommand\kowalskiname    {\kowalskiindex{\namefont \robert\ A. \kowalski}}
\newcommand\kowalskilifetime{(*1941)}
\newcommand\knaster         {{\namefont Knaster}}
\newcommand\knastername     {{\namefont Bronis\l aw \knaster}}
\newcommand\knasterlifetime {(1893--1990)}
\newcommand\knastertarski   {\knaster--\tarski}
\newcommand\kneser          {{\namefont Kneser}}
\newcommand\kneserzweiname  {{\namefont Hellmuth \kneser}}
\newcommand\kneserzweilifetime{(1898--1973)}
\newcommand\kreiselindex                 {\index{Kreisel, Georg (1923--2014)}}
\newcommand\protectedkreiselindex{\protect\index{Kreisel, Georg (1923--2014)}}
\newcommand\kreisel         {{\namefont Kreisel}}
\newcommand\kreiselnamenoindex{{\namefont\georg\ \kreisel}}
\newcommand\kreiselname     {\kreiselindex\kreiselnamenoindex}
\newcommand\kreisellifetime {(1923--2014)}
\newcommand\kreowski        {{\namefont Kreow\-ski}}
\newcommand\kreowskiname    {{\namefont\hans-\joerg\ \kreowski}}
\newcommand\kroneckerindex  {\index{Kronecker, Leopold (1823--1891)}}
\newcommand\kronecker       {\mbox{\namefont Kronecker}}
\newcommand\kroneckername   {\kroneckerindex{\namefont\leopold\ \kronecker}}
\newcommand\kroneckerlifetime{(1823--1891)}
\newcommand\kruskal         {Kruskal}
\newcommand\kruskalname     {\joseph\ B. \kruskal}
\newcommand\kuechlin        {K\ue ch\-lin}
\newcommand\kuechlinname    {\wolfgang\ \kuechlin}
\newcommand\kuehlerindex    {\index
                            {Kuehler, Ulrich (*1964)@{K\"uhler, Ulrich (*1964)}}}
\newcommand\protectedkuehlerindex{\protect\index
                            {Kuehler, Ulrich (*1964)@{K\"uhler, Ulrich (*1964)}}}
\newcommand\kuehler         {{\namefont K\ue h\-ler}}
\newcommand\kuehlername     {\kuehlerindex{\namefont\ulrich\ \kuehler}}
\newcommand\kuehlerlifetime {(*1964)}
\newcommand\kuhn            {{\namefont Kuhn}}
\newcommand\kuhnname        {{\namefont\thomas\ S. \kuhn}}
\newcommand\kuhnlifetime    {(1922--1996)}
\newcommand\kummer          {Kummer}
\newcommand\kummername      {\ernst\ Eduard \kummer}
\newcommand\kummerlifetime  {(1810--1893)}
\newcommand\kuratowskiindex {\index{Kuratowski, Kazimierz (1896--1980)}}
\newcommand\kuratowski      {{\namefont Kuratowski}}
\newcommand\kuratowskiname  {\kuratowskiindex{\namefont\kazimierz\ \kuratowski}}
\newcommand\kuratowskilifetime{(1896--1980)}
\newcommand\lambert         {{\namefont Lambert}}
\newcommand\lambertname     {{\namefont\edmund\ \johann\ \heinrich\ \lambert}}
                           % G. H. = Georg Hermann
\newcommand\lambertlifetime {(1728--1777)}
\newcommand\lambertdiagram  {\lambert\ diagram}
\newcommand\landau          {{\namefont\Landau}}
\newcommand\landauname      {{\namefont\edmund\ G. H. \landau}}
                           % G. H. = Georg Hermann
\newcommand\landaulifetime  {(1877--1938)}
\newcommand\lankford        {Lankford}
\newcommand\lankfordname    {Dalla\es\ S. \lankford}
\newcommand\laotse          {Lao\-zi}
\newcommand\laotsename      {\laotse}
\newcommand\taoteking       {Tao Te King}
\newcommand\lautmanindex    {\index{Lautman, Albert (1908--1944)}}
\newcommand\protectedlautmanindex
                    {\protect\index{Lautman, Albert (1908--1944)}}
\newcommand\lautman         {{\namefont Laut\-man}}
\newcommand\lautmanname     {\lautmanindex{\namefont\albert\ \lautman}}
\newcommand\lautmanlifetime {(1908--1944)}
\newcommand\lavoisier       {La\-voi\-sier}
\newcommand\lavoisiername   {Antoine Laurent de \lavoisier}
\newcommand\lavoisierlifetime{(1743--1794)}
\newcommand\lee             {Lee}
\newcommand\leename         {\richard\ C.-T. \lee}
\newcommand\leeuwen         {Leeuwen}
\newcommand\leeuwenname     {\jan\ van \leeuwen}
\newcommand\lehmann         {{\namefont Lehmann}}
\newcommand\lehmannname     {{\namefont Daniel \lehmann}}
\newcommand\leibniz         {{\namefont Leibniz}}
\newcommand\leibnizname     {{\namefont \gottfried\ \wilhelm\ \leibniz}}
\newcommand\leibnizlifetime {(1646--1716)}
\newcommand\leisenring      {{\namefont Leisen\-ring}}
\newcommand\leisenringname  {{\namefont\leisenringfirstname\ \leisenring}}
\newcommand\leisenringfirstname
                            {\albert\ C.}
                            %{Al C.}
                            %{A. C.}
                            %{Al(bert) C.}
\newcommand\leisenringlifetime{(*1941?)}
\newcommand\leibowitz       {Leibowitz}
\newcommand\leibowitzname   {\rene\ \leibowitz}
\newcommand\leibowitzlifetime{(1913--1972)}
\newcommand\leitsch         {{\namefont Leitsch}}
\newcommand\leitschname     {{\namefont\alexander\ \leitsch}}
\newcommand\lenart          {{\namefont Lenart}}
\newcommand\lenartname      {{\namefont Mihaly \lenart}}
\newcommand\lesniewskiindex {\index{Le\'sniewski, Stanis\l aw (1886--1939)}}
\newcommand\protectedlesniewskiindex
                    {\protect\index{Le\'sniewski, Stanis\l aw (1886--1939)}}
\newcommand\lesniewski      {{\namefont Le\'sniewski}}
\newcommand\lesniewskiname  {\lesniewskiindex{\namefont\stanislaw\ \lesniewski}}
\newcommand\lesniewskilifetime{(1886--1939)}
\newcommand\letz            {{\namefont Letz}}
\newcommand\letzname        {{\namefont Rein\-hold \letz}}
\newcommand\levyname        {\jean-\jacques\ L\'evy}
\newcommand\lewi            {{\namefont Lewi}}
\newcommand\lewiname        {{\namefont\johan\ \lewi}}
\newcommand\lewisindex      {\index{Lewis, Clarence Irving (1883--1964)}}
\newcommand\protectedlewisindex
                    {\protect\index{Lewis, Clarence Irving (1883--1964)}}
\newcommand\lewis           {{\namefont Lewis}}
\newcommand\lewisname       {\lewisindex{\namefont Clarence \irving\ \lewis}}
\newcommand\lewislifetime   {(1883--1964)}
\newcommand\lewy            {{\namefont Lewy}}
\newcommand\lewyname        {{\namefont\hans\ \lewy}}
\newcommand\lewylifetime    {(1904--1980)}
\newcommand\lifschitz       {{\namefont Lifschitz}}
\newcommand\lifschitzname   {{\namefont\vladimir\ A. \lifschitz}}
\newcommand\lipschitz       {{\namefont Lipschitz}}
\newcommand\lipschitzname   {{\namefont\rudolf\ \lipschitz}}
\newcommand\lipschitzlifetime{1832--1903}
\newcommand\lindner         {{\namefont Lindner}}
\newcommand\lindnername     {{\namefont\wolfgang\ \lindner}}
\newcommand\linne           {{\namefont Linn\'e}}
\newcommand\linnename       {{\namefont\carl\ von \linne}}
\newcommand\linnelifetime   {(1707--1778)}
\newcommand\loechnerindex   {\index
                           {Loechner, Bernd (*1967)@{L\"ochner, Bernd (*1967)}}}
\newcommand\protectedloechnerindex{\protect\index
                           {Loechner, Bernd (*1967)@{L\"ochner, Bernd (*1967)}}}
\newcommand\loechner        {{\namefont L\oe chner}}
\newcommand\loechnername    {\loechnerindex{\namefont\bernd\ \loechner}}
\newcommand\loechnerlifetime{(*1967)}
\newcommand\loewenheimindex {\index
{Loewenheim@L\"owenheim, Leopold (1878--1957)}}
\newcommand\loewenheimindexstart{\index
{Loewenheim@L\"owenheim, Leopold (1878--1957)|(}}
\newcommand\loewenheimindexend{\index
{Loewenheim@L\"owenheim, Leopold (1878--1957)|)}}
\newcommand\protectedloewenheimindex{\protect\index
{Loewenheim@L\"owenheim, Leopold (1878--1957)}}
\newcommand\loewenheim      {{\namefont L\oe wen\-heim}}
\newcommand\loewenheimname  {\loewenheimindex{\namefont\leopold\ \loewenheim}}
\newcommand\loewenheimlifetime{(1878--1957)}
\newcommand\loewenheimskolem{\loewenheim--\skolem}
\newcommand\loewenheimskolemtheorem{\index
                    {Loewenheim-Skolem Theorem@L{\oe}wenheim--Skolem Theorem}%
                                                     \loewenheimskolem\ Theorem}
\newcommand\loewenheimskolemtheoremindexbegin{\index
                    {Loewenheim-Skolem Theorem@L{\oe}wenheim--Skolem Theorem|(}}
\newcommand\loewenheimskolemtheoremindexend{\index
                    {Loewenheim-Skolem Theorem@L{\oe}wenheim--Skolem Theorem|)}}
\newcommand\upwardloewenheimskolemtarskitheorem{\index
{Loewenheim-Skolem-Tarski Theorem@L{\oe}wenheim--Skolem--Tarksi Theorem!Upward}%
                                     Upward \loewenheimskolem--\tarski\ Theorem}
\newcommand\loefindex       {\index{Martin-L\"of, Per (*1942)}}
\newcommand\loef            {{\namefont\martin-L\oe f}}
\newcommand\loefname        {\loefindex{\namefont Per \loef}}
\newcommand\loeflifetime    {(*1942)}
\newcommand\loria           {Lor\'\i a-S\'aenz}
\newcommand\lorianame       {\carlos\ A. \loria}
\newcommand\liouville       {Liouville}
\newcommand\liouvillename   {\joseph\ \liouville}
\newcommand\liouvillelifetime{(1809--1882)}
\newcommand\lukasiewiczindex
                        {\index{Lukasiewicz@\L uka\-sie\-wicz, Jan (1878--1956)}}
\newcommand\lukasiewicz     {{\namefont \L uka\-sie\-wicz}}
\newcommand\lukasiewiczname {\lukasiewiczindex{\namefont\jan\ \lukasiewicz}}
\newcommand\lukasiewiczlifetime{(1878--1956)}
\newcommand\titlelukasiewicztarski 
          {Unter\-suchungen \ue ber den Au\esi sagen\-kalk\ue l}
\newcommand\lunde           {{\namefont Lunde}}
\newcommand\lundename       {{\namefont\ruediger\ \lunde}}
\newcommand\luther          {{\namefont Luther}}
\newcommand\luthername      {{\namefont\martin\ \luther}}
\newcommand\lutherlifetime  {(1483--1546)}
\newcommand\lynchindex      {\index{Lynch, Christopher}}
\newcommand\lynch           {{\namefont Lynch}}
\newcommand\lynchname       {\lynchindex{\namefont Christopher \lynch}}
\newcommand\maclane         {{\namefont MacLane}}
\newcommand\maclanename     {{\namefont Saunders \maclane}}
\newcommand\maclanelifetime {(1909--2005)}
\newcommand\macqueen        {MacQueen}
\newcommand\macqueenname    {\david\ B. \macqueen}
\newcommand\madlener        {{\namefont Mad\-lener}}
\newcommand\madlenername    {{\namefont\klaus\ \madlener}}
\newcommand\mahr            {{\namefont Mahr}}
\newcommand\mahrname        {{\namefont\bernd\ \mahr}}
\newcommand\majer           {{\namefont Majer}}
\newcommand\majername       {{\namefont\ulrich\ \majer}}
\newcommand\makinson        {{\namefont Makinson}}
\newcommand\makinsonname    {{\namefont\david\ \makinson}}
\newcommand\mancosu         {{\namefont Mancosu}}
\newcommand\mancosuname     {{\namefont\paolo\ \mancosu}}
\newcommand\mann            {{\namefont Mann}}
\newcommand\mannname        {{\namefont\thomas\ \mann}}
\newcommand\mannlifetime    {(1875--1955)}
\newcommand\manna           {Manna}
\newcommand\mannaname       {Zohar \manna}
\newcommand\manolios        {{\namefont Manolio\es}}
\newcommand\manoliosname    {{\namefont Panagioti\es\ ``Pete'' \manolios}}
\newcommand\marx            {{\namefont Marx}}
\newcommand\marxname        {{\namefont\karl\ \marx}}
\newcommand\maslov          {{\namefont Maslov}}
\newcommand\maslovname      {{\namefont\sergey\ Yu.\ \maslov}}
\newcommand\mattick         {{\namefont Mattick}}
\newcommand\mattickname     {{\namefont\volker\ \mattick}}
\newcommand\maurolycusindex {\index{Maurolico, Francesco (1494--1575)}} 
\newcommand\maurolycus      {{\namefont Maurolico}}
\newcommand\maurolycuslatin {{\namefont Maurolycu\es}}
\newcommand\maurolycusname  {\maurolycusindex{\namefont Francesco \maurolycus}}
\newcommand\maurolycuslifeplace{Messina}
\newcommand\maurolycuslifetime{(1494--1575)}
\newcommand\mccarthyindex   {\index{McCarthy, John (1927--2011)}}
\newcommand\mccarthy        {\mbox{\namefont McCarthy}}
\newcommand\mccarthyname    {\mccarthyindex{\namefont\john\ \mccarthy}}
\newcommand\mccarthylifetime{(1927--2011)}
\newcommand\mcguinnessbfindex{\index{McGuinness, Brian Francis}}
\newcommand\mcguinness      {\mbox{\namefont McGuinness}}
\newcommand\mcguinnessbfname
                        {\mcguinnessbfindex{\namefont Brian Francis \mcguinness}}
\newcommand\meier           {{\namefont Meier}}
\newcommand\meiername       {{\namefont\andreas\ \meier}}
\newcommand\meinong         {{\namefont Meinong}}
\newcommand\meinongname     {{\namefont Alexiu\es\ \meinong}}
\newcommand\meinonglifetime {(1853--1920)}
\newcommand\Gegenstand      {Gegen\-stand}
\newcommand\Gegenstandstheorie{\Gegenstand\esi theo\-rie}
\newcommand\melisindex      {\index{Melis, Erica (1949--2011)}}
\newcommand\melis           {{\namefont Meli\es}}
\newcommand\melisname       {\melisindex{\namefont Erica \melis}}
\newcommand\melislifetime   {(1949--2011)}
\newcommand\mendelssohn     {{\namefont Mendel\esi sohn}}
\newcommand\mendelssohnname {{\namefont Moses \mendelssohn}}
\newcommand\mendelssohnlifetime{(1729--1786)}
\newcommand\meseguer        {Meseguer}
\newcommand\meseguername    {\jose\ \meseguer}
\newcommand\meyerviol       {{\namefont Meyer-Viol}}
\newcommand\meyerviolname   {{\namefont\wilfried\ P. M. \meyerviol}}
\newcommand\meltzerindex    {\index{Meltzer, Bernard (1916?--2008)}}
\newcommand\protectedmeltzerindex{\protect\index{Meltzer, Bernard (1916?--2008)}}
\newcommand\meltzer         {{\namefont Meltzer}}
\newcommand\meltzername     {\meltzerindex{\namefont \bernard\ \meltzer}}
\newcommand\meltzerlifetime {(1916?--2008)}
\newcommand\menzler         {{\namefont Menzler}}
\newcommand\menzlername     {{\namefont Eckhart \menzler}}
\newcommand\michieindex     {\index{Michie, Donald (1923--2007)}}
\newcommand\protectedmichieindex{\protect\index{Michie, Donald (1923--2007)}}
\newcommand\michie          {{\namefont Michie}}
\newcommand\michiename      {\michieindex{\namefont\donald\ \michie}}
\newcommand\michielifetime  {(1923--2007)}
\newcommand\middeldorp      {Middel\-dorp}
\newcommand\middeldorpname  {Aart \middeldorp}
\newcommand\miller          {{\namefont Miller}}
\newcommand\millername      {{\namefont Dale A. \miller}} 
% {Dale \miller} As his supervisor Peter Andrews
% cites him with middle initial, we had better do so, too
\newcommand\milnerindex     {\index{Milner, Robin (1934--2010)}}
\newcommand\milner          {{\namefont Milner}}
\newcommand\milnername      {\milnerindex{\namefont\robin\ \milner}} 
\newcommand\milnerlifetime  {(1934--2010)}
\newcommand\minsky          {{\namefont Minsky}}
\newcommand\minskyname      {{\namefont\marvin\ \minsky}} 
\newcommand\minskylifetime  {(*1927)}
\newcommand\mints           {Mint\es}
\newcommand\mintsname       {{\namefont Grigori    \mints}}
%                           {{\namefont Grigori E. \mints}}
\newcommand\mintslifetime   {(1939--2014)}
\newcommand\mitchell        {Mitchell}
\newcommand\mitchellname    {Oscar \howard\ \mitchell} 
\newcommand\mitchelllifetime{(1851--1889)}
\newcommand\mitchelldeathdate{\Mar\,29, 1889}
\newcommand\mitchelldeathcourse{pneumonia}
% Lungenentzuendung, Quelle: Peirce, Chronological Edition, Vol. 6, p.lvi
\newcommand\montanari       {{\namefont Montanari}}
\newcommand\montanariname   {{\namefont Ugo \montanari}}
\newcommand\mooreindex      {\index{Moore, J Strother (*1947)}}
\newcommand\moore           {{\namefont Moore}}
\newcommand\moorenamenoindex{{\namefont J~Strother \moore}}
% J does not want to have S. instead of Strother
\newcommand\moorename       {\mooreindex\moorenamenoindex}
\newcommand\moorelifetime   {(*1947)}
\newcommand\mooreswifename  {{\namefont Jo \moore}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand\mooregeindex    {\index{Moore, G. E. (1873--1958)}}
\newcommand\mooregename     {\mooregeindex{\namefont G. E. \moore}}
\newcommand\mooregelifetime {(1873--1958)}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand\mooreghindex    {\index{Moore, Gregory H. (*1944)}}
\newcommand\protectedmooreghindex{\protect\index{Moore, Gregory H. (*1944)}}
\newcommand\mooreghname     {\mooregeindex{\namefont Gregory H. \moore}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand\morse           {{\namefont Morse}}
\newcommand\morsename       {{\namefont Anthony P.    \morse}}
%                           {{\namefont Anthony Percy \morse}}
\newcommand\morselifetime   {(1911--1984)}
\newcommand\MKlong          {\morse--\kelley}
\newcommand\MKshort         {{\sc MK}}
\newcommand\moschnerindex   {\index{Moschner, Markus}}
\newcommand\moschner        {{\namefont Moschner}}
\newcommand\moschnername    {\moschnerindex{\namefont\markus\ \moschner}}
\newcommand\moser           {{\namefont Moser}}
\newcommand\mosername       {{\namefont\georg\ Ch.\ \moser}}
\newcommand\moss            {{\namefont Mo\ses}}
\newcommand\mossname        {{\namefont\lawrence\ \moss}}
\newcommand\mostowski       {{\namefont Mostowski}}
\newcommand\mostowskiname   {{\namefont Andrzej \mostowski}}
\newcommand\mostowskilifetime{(1913--1975)}
\newcommand\mozart          {\mbox{\namefont Mozart}}
\newcommand\mozartname      {{\namefont\wolfgang\ Amadeus \mozart}}
\newcommand\mozartlifetime  {(1756--1791)}
\newcommand\mueller         {{\namefont M\ue ller}}
\newcommand\muellername     {{\namefont Gert H. \mueller}}
\newcommand\musser          {{\namefont Musser}}
\newcommand\mussername      {{\namefont\david\ R. \musser}}
\newcommand\nagelindex      {\index{Nagel, Ernest (1901--1985)}}
\newcommand\nagel           {{\namefont Nagel}}
\newcommand\nagelname       {\nagelindex{\namefont\ernest\ \nagel}}
\newcommand\nagellifetime   {(1901--1985)}
\newcommand\narendran       {Narendran}
\newcommand\narendranname   {Paliath \narendran}
\newcommand\nebel           {Nebel}
\newcommand\nebelname       {\bernhard\ \nebel}
\newcommand\nedoindex       {\index{Nedo, Michael (1940)}}
\newcommand\protectednedoindex{\protect\index{Nedo, Michael (1940)}}
\newcommand\nedo            {{\namefont Nedo}}
\newcommand\nedoname        {\nedoindex{\namefont\michaelwithouttrema\ \nedo}}
\newcommand\nedolifetime    {(*1940)}
\newcommand\nelsoneinsindex {\index{Nelson, Leonard (1921--2006)}}
\newcommand\nelson          {{\namefont Nelson}}
\newcommand\nelsoneinsname  {\nelsoneinsindex{\namefont Leonard \nelson}}
\newcommand\nelsoneinslifetime{(1921--2006)}
\newcommand\neumannindex    {\index{Neumann, John von (1903--1957)}}
\newcommand\protectedneumannindex
                    {\protect\index{Neumann, John von (1903--1957)}}
\newcommand\neumann         {{\namefont Neumann}}
\newcommand\neumannname     {\neumannindex{\namefont\john\ von \neumann}}
%                           {{\namefont\john\ L. von \neumann}}
\newcommand\neumannlifetime {(1903--1957)}
\newcommand\NBGlong         {\neumann--\bernays--\goedel}
\newcommand\NBGshort        {{\sc NBG}}
\newcommand\newmanindex     {\index{Newman, Max(well) H. A. (1897--1984)}}
\newcommand\protectednewmanindex
                           {\protect\index{Newman, Max(well) H. A. (1897--1984)}}
\newcommand\newman          {{\namefont Newman}}
\newcommand\newmanname      {\newmanindex{\namefont Max~H.~A. \newman}}
\newcommand\newmanlemma     {\index{Newman Lemma}\newman\ Lemma}
\newcommand\newmanlifetime  {(1897--1984)}
\newcommand\newtonindex     {\index{Newton, Isaac (1643--1727)}}
\newcommand\newton          {{\namefont Newton}}
\newcommand\newtonname      {\newtonindex{\namefont Isaac \newton}}
\newcommand\newtonlifetime  {(1643--1727)}
\newcommand\nicolosi        {{\namefont Nicolosi-Asmundo}}
\newcommand\nicolosiname    {{\namefont Marianna \nicolosi}}
\newcommand\nieuwenhuis     {Nieuwenhui\es}
\newcommand\nieuwenhuisname {\robert\ \nieuwenhuis}
\newcommand\nipkow          {{\namefont Nipkow}}
\newcommand\nipkowname      {{\namefont\tobias\ \nipkow}}
\newcommand\nicodindex      {\index{Nicod, Jean (1893--1924)}}
\newcommand\protectednicodindex
                    {\protect\index{Nicod, Jean (1893--1924)}}
\newcommand\nicod           {{\namefont Nicod}}
\newcommand\nicodname       {\nicodindex{\namefont\jean\ \nicod}}
\newcommand\nicodlifetime   {(1893--1924)}
\newcommand\nicolauscusanus {\nicolaus}
\newcommand\nicolauscusanusname{\nicolauscusanus\ of Cu\ewithtrema\es}
\newcommand\nicolauscusanuslifetime{(1401--1464)}
\newcommand\noetherindex                 {\index{Noether, Emmy (1882--1935)}}
\newcommand\protectednoetherindex{\protect\index{Noether, Emmy (1882--1935)}}
\newcommand\noether         {{\namefont Noether}}
%                           {{\namefont N\oe ther}}
% Though ``N\oe ther'' is also definitely correct as a ligature and is also
% the version of the birth certificate of Emmy,
% in the old age Max and in her adult age Emmy never used the 
% umlaut
\newcommand\noethername     {\noetherindex{\namefont    \emmy\ \noether}}
%                           {\noetherindex{\namefont A. \emmy\ \noether}}
\newcommand\noetherfathername{\maxchristianname\ \noether}
\newcommand\noetherbirthyear{1882}
\newcommand\noetherdeathyear{1935}
\newcommand\noetherlifetime {(\noetherbirthyear--\noetherdeathyear)}
\newcommand\noetherfatherlifetime{(1844--1921)}
\newcommand\noetherian      {\noether\-ian}
\newcommand\theoremofnoetherianinduction{\index
{induction!Noetherian}Theorem of\/ \noetherian\ Induction}
\newcommand\structuralinductionindex{\index{induction!structural}}
\newcommand\axiomofstructuralinductionfirsthalf{Axiom}
\newcommand\axiomofstructuralinductionsecondhalf
                            {\structuralinductionindex of Structural Induction}
\newcommand\axiomofstructuralinduction{\axiomofstructuralinductionfirsthalf\ 
\axiomofstructuralinductionsecondhalf}
\newcommand\axiomofchoice   {\index{choice!Axiom of Choice}Axiom of Choice}
\newcommand\axiomofcollection{Axiom of Collection}
\newcommand\nonnengart      {{\namefont Nonnengart}}
\newcommand\nonnengartname  {{\namefont\andreas\ \nonnengart}}
\newcommand\nourani         {Nourani}
\newcommand\nouraniname     {Cyru\es\ F. \nourani}
\newcommand\okadaname       {{\namefont Mitsuhiro Okada}}
\newcommand\ockham          {{\namefont Ockham}}
\newcommand\ockhamname      {{\namefont \william\ of \ockham}}
\newcommand\ockhamlifetime  {(1285--1347)}
\newcommand\oostrom         {{\namefont Oostrom}}
\newcommand\oostromname     {{\namefont Vincent van \oostrom}}
\newcommand\orevkov         {Orevkov}
\newcommand\orevkovname     {\vladimir\ P. \orevkov}
\newcommand\ottoname        {\friedrich\ \ottonoconflict}
\newcommand\padawitz        {{\namefont Pada\-witz}}
\newcommand\padawitzname    {{\namefont\peter\ \padawitz}}
\newcommand\padoaindex      {\index{Padoa, Alessandro (1868--1937)}}
\newcommand\protectedpadoaindex{\protect\index{Padoa, Alessandro (1868--1937)}}
\newcommand\padoa           {{\namefont Padoa}}
\newcommand\padoaname       {\padoaindex{\namefont Alessandro \padoa}}
\newcommand\padoalifetime   {(1868--1937)}
\newcommand\paley           {{\namefont Paley}}
\newcommand\paleyname       {{\namefont\raymond\ \paley}}
\newcommand\paleylifetime   {(1907--1933)}
\newcommand\pandora         {Pandora}
\newcommand\parsonsindex    {\index{Parsons, Charles (*1933)}}
\newcommand\parsons         {{\namefont Parsons}}
\newcommand\parsonsname     {\parsonsindex{\namefont\charles\ \parsons}}
\newcommand\parsonslifetime {(*1933)}
\newcommand\pascalindex     {\index{Pascal, Blaise (1623--1662)}}
\newcommand\pascal          {{\namefont Pascal}}
\newcommand\pascalname      {\pascalindex{\namefont Blaise \pascal}}
\newcommand\pascalbirthyear {1623}
\newcommand\pascaldeathyear {1662}
\newcommand\pascallifetime  {(\pascalbirthyear--\pascaldeathyear)}
\newcommand\pasztor         {Pasztor}
\newcommand\pasztorname     {Ana \pasztor}
\newcommand\paterson        {Paterson}
\newcommand\patersonname    {\michaelwithouttrema\ S. \paterson}
\newcommand\paulson         {{\namefont Paulson}}
\newcommand\paulsonname     {{\namefont\lawrence\ C. \paulson}}
%                           {Larry C. \paulson}
% Larry will das so!
\newcommand\peanoindex      {\index{Peano, Guiseppe (1858--1932)}}
\newcommand\peanoaxiomsindex{\index{Peano axioms}}
\newcommand\peano           {{\namefont Peano}}
\newcommand\peanoname       {\peanoindex{\namefont Guiseppe \peano}}
\newcommand\peanolifetime   {(1858--1932)}
\newcommand\peanoaxiom      {\peanoaxiomsindex\peano\ axiom}
\newcommand\peckhausindex                 {\index{Peckhaus, Volker (*1955)}}
\newcommand\protectedpeckhausindex{\protect\index{Peckhaus, Volker (*1955)}}
\newcommand\peckhaus        {{\namefont Peck\-haus}}
\newcommand\peckhausname    {\peckhausindex{\namefont \volker\ \peckhaus}}
\newcommand\peckhauslifetime{(*1955)}
\newcommand\peirceindex     {\index{Peirce, Charles S. (1839--1914)}}
\newcommand\protectedpeirceindex
                    {\protect\index{Peirce, Charles S. (1839--1914)}}
\newcommand\peirce          {{\namefont Peirce}}
\newcommand\peircename      {\peirceindex{\namefont \charles\ S. \peirce}}
                           %{\charles\ Sanders \peirce}
\newcommand\peircelifetime  {(1839--1914)}
\newcommand\peircefathername{\benjamin\ \peirce}
\newcommand\peircefatherlifetime{(1809--1880)}
\newcommand\peirceslawindex {\index{Peirce's Law}}
\newcommand\peirceslaw      {\peirceslawindex\peirce's Law}
\newcommand\peterindex      {\index{P\'eter, R\'osza (1905--1977)}}
\newcommand\protectedpeterindex{\protect\index{P\'eter, R\'osza (1905--1977)}}
\newcommand\peterrosza      {{\namefont P\'eter}}
\newcommand\petername       {\peterindex{\namefont R\'osza \peterrosza}}
\newcommand\peterlifetime   {(1905--1977)}
\newcommand\peters          {Peter\es}
\newcommand\petersname      {\stanley\ \peters}
\newcommand\bachpeterssentence{\bach--\peters\ sentence}
\newcommand\bachpetersSentence{\bach--\peters\ Sentence}
\newcommand\peterson        {Peterson}
\newcommand\petersonname    {\john\ \peterson}
\newcommand\pieriindex      {\index{Pieri, Mario (1860--1913)}}
\newcommand\pieri           {{\namefont Pieri}}
\newcommand\pieriname       {\pieriindex{\namefont Mario \pieri}}
\newcommand\pierilifetime   {(1860--1913)}
\newcommand\pinkal          {Pinkal}
\newcommand\pinkalname      {\manfred\ \pinkal}
\newcommand\philo           {{\namefont Philo}}
\newcommand\philoname       {{\namefont\philo\ the Dialectician}}
% Also called "Philo of Megara", but not from Megara
\newcommand\philolifetime   {(\ca\ 300\BC)}
\newcommand\Philonian       {\philo nian}
\newcommand\plaisted        {{\namefont Plaisted}}
\newcommand\plaistedname    {{\namefont\david\ A. \plaisted}}
\newcommand\planckindex     {\index{Planck, Max (1858--1947)}}
\newcommand\plancknonamefont{Planck}
\newcommand\planck          {{\namefont\plancknonamefont}}
\newcommand\plancknamenonamefont{\maxchristiannamenonamefont\ \plancknonamefont}
\newcommand\planckname      {\planckindex{\namefont\plancknamenonamefont}}
\newcommand\plancklifetime  {(1858--1947)}
\newcommand\platoindex      {\index{Plato (427--347\,\BC)}}
\newcommand\plato           {{\namefont Plato}}
\newcommand\platoname       {\platoindex\plato} 
                            % Plato is a nickname ``the broad''.
\newcommand\platolifetime   {(427--347\,\BC)}
\newcommand\plotkin         {{\namefont Plotkin}}
\newcommand\plotkinname     {{\namefont Gordon \plotkin}}
\newcommand\plotkinlifetime {(*1946)}
\newcommand\popplestoneindex{\index{Popplestone, Robin J. (1938--2004)}}
\newcommand\popplestone     {{\namefont Popplestone}}
\newcommand\popplestonename {{\namefont\robin\ J. \popplestone}}
\newcommand\popplestonelifetime{(1938--2004)}
\newcommand\poincareindex   {\index{Poincar\'e, Henri (1854--1912)}}
\newcommand\poincare        {{\namefont Poincar\'e}}
\newcommand\poincarename    {\poincareindex{\namefont Henri \poincare}}
\newcommand\poincarelifetime{(1854--1912)}
\newcommand\poole           {{\namefont Poole}}
\newcommand\poolename       {{\namefont\david\ \poole}}
\newcommand\popper          {{\namefont\mbox{Popper}}}
\newcommand\poppername      {{\namefont\karl\ \popper}}
                           %{\karl\ R. \popper} 
\newcommand\popperlifetime  {(1902--1994)}
\newcommand\post            {{\namefont Post}}
\newcommand\postname        {{\namefont\emil\ \leon\ \post}}
\newcommand\postlifetime    {(1987--1954)}
\newcommand\pollet          {{\namefont Pollet}}
\newcommand\polletname      {{\namefont\martin\ \pollet}}
\newcommand\prause          {Prause}
\newcommand\prausename      {\gerhard\ \prause}
\newcommand\prawitz         {{\namefont Pra\-witz}}
\newcommand\prawitzname     {{\namefont Dag \prawitz}}
\newcommand\presburgerindex {\index{Presburger, Moj{\.z}es{}z (1904--1943?)}}
\newcommand\protectedpresburgerindex{\protect\index
                                   {Presburger, Moj{\.z}es{}z (1904--1943?)}}
\newcommand\presburger      {{\namefont Pre\esi burger}} %actually: Prezburger
\newcommand\presburgername  
               {\presburgerindex{\namefont\mbox{Moj\zwithdot es{}z} \presburger}}
\newcommand\presburgerlifetime{(1904--1943?)}
\newcommand\presburgerarithmetic{\presburger\ Arithmetic}
\newcommand\presburgertruename{Prez\-burger}
\newcommand\priestley       {Priestley}
\newcommand\priestleyname   {\joseph\ \priestley}
\newcommand\priestleylifetime{(1733--1804)}
\newcommand\prote           {{\namefont Prote}}
\newcommand\protename       {{\namefont\horst\ \prote}}
\newcommand\protzenindex    {\index{Protzen, Martin (*1962)}}
\newcommand\protectedprotzenindex{\protect\index{Protzen, Martin (*1962)}}
\newcommand\protzen         {{\namefont Protzen}}
\newcommand\protzenname     {\protzenindex{\namefont\martin\ \protzen}}
\newcommand\protzenlifetime {(*1962)}
\newcommand\ptolemaios      {Ptole\-maio\es}
\newcommand\ptolemaiosname  {Klaudio\es\ \ptolemaios}
\newcommand\ptolemaioslifetime{(\ca\,100--\ca\,160)}
\newcommand\putnam          {{\namefont Putnam}}
\newcommand\putnamname      {{\namefont Hilary \putnam}}
\newcommand\putnamlifetime  {(*1926)}
\newcommand\pythagoras      {Pythagora\es}
\newcommand\pythagorasname  {\pythagoras}
%                           {\pythagoras\ of Samo\es}
% As the only other Pythagoras is also from Samos, what does ``of Samos'' help?
\newcommand\pythagoraslifetime{(\ca\,570--\ca\,500\BC)}
\newcommand\pythagorean     {{\namefont Pytha\-gorean}}
\newcommand\pythagoreans    {{\namefont\pythagorean s}}
\newcommand\quineindex      {\index{Quine, Willard Van O. (1908--2000)}}
\newcommand\quine           {{\namefont Quine}}
\newcommand\quinename       {\quineindex{\namefont Willard Van O. \quine}}
%                           {{\namefont Willard Van %Orman \quine}}
\newcommand\quinelifetime   {(1908--2000)}
\newcommand\raamsdonk       {Raams\-donk}
\newcommand\raamsdonkname   {Femke van \raamsdonk}
\newcommand\readiname       {Rodrigo Readi-Nasser}
\newcommand\reddy           {Reddy}
\newcommand\reddyname       {Uday S. \reddy}
\newcommand\reichel         {Rei\-chel}
\newcommand\reichelname     {\horst\ \reichel}
\newcommand\reyle           {Reyle}
\newcommand\reylename       {\uwe\ \reyle}
\newcommand\rezaeiindex     {\index{Rezaei, Marianeh (*1980)}}
\newcommand\rezaei          {{\namefont Rezaei}}
\newcommand\rezaeinamenoindex{{\namefont Marianeh \rezaei}} 
\newcommand\rezaeiname      {\rezaeiindex\rezaeinamenoindex}
\newcommand\rezaeilifetime  {(*1980)}
\newcommand\rheesindex      {\index{Rhees, Rush (1905--1989)}}
\newcommand\rhees           {{\namefont Rhees}}
\newcommand\rheesname       {{\namefont Rush \rhees}}
\newcommand\rheeslifetime   {(1905--1989)}
\newcommand\ribet           {{\namefont Ribet}}
\newcommand\ribetname       {{\namefont Ken \ribet}} 
                           %{Kenneth A. \ribet}
\newcommand\riemannindex    {\index{Riemann, Bernhard (1826--1866)}}
\newcommand\riemann         {{\namefont Rie\-mann}}
\newcommand\riemannname     {{\namefont\bernhard\ \riemann}}
\newcommand\riemannlifetimenoparentheses{1826--1866}
\newcommand\riemannlifetime {(\riemannlifetimenoparentheses)}
\newcommand\ritchie         {Ritchie}
\newcommand\ritchiename     {Denni\es\ M. \ritchie}
\newcommand\robbins         {{\namefont Robbin\es}}
\newcommand\robbinsname     {{\namefont\herbert\ E. \robbins}}
\newcommand\robbinslifetime {(1922--2001)}
\newcommand\robbinsproblem  {\robbins\ Algebra problem}
\newcommand\robinsonindex   {\index{Robinson, J. Alan (*1930?)}}
\newcommand\protectedrobinsonindex{\protect\index{Robinson, J. Alan (*1930?)}}
\newcommand\robinson        {{\namefont Robinson}}
\newcommand\robinsonname    {\robinsonindex{\namefont J.\hskip.25em\alan\ \robinson}}
\newcommand\robinsonlifetime{(*1930?)}
\newcommand\robinsontwoname {\peter\ J. \robinson}
\newcommand\roch            {{\namefont Roch}}
\newcommand\rochname        {{\namefont\gustav\ \roch}}
\newcommand\rochlifetime    {(1839--1866)}
\newcommand\roedding        {{\namefont R\oe dding}}
\newcommand\roeddingname    {{\namefont\dieter\ \roedding}}
\newcommand\rosu            {Ro\c su}
\newcommand\rosuname        {Grigore \rosu}
\newcommand\reinert         {Reinert}
\newcommand\reinertname     {Birgit \reinert}
\newcommand\roentgen        {R\oe ntgen}
\newcommand\roentgenname    {\wilhelm \ \roentgen}
\newcommand\roquetteindex   {\index{Roquette, Peter (*1927)}}
\newcommand\protectedroquetteindex{\protect\index{Roquette, Peter (*1927)}}
\newcommand\roquette        {{\namefont Roquette}}
\newcommand\roquettename    {\roquetteindex{\namefont\peter\ \roquette}}
\newcommand\rosserindex     {\index{Rosser, Barkley (1907--1989)}}
\newcommand\rosser          {{\namefont Rosser}}
\newcommand\rossername      {{\namefont    Barkley \rosser}}
                           %{{\namefont J. Barkley \rosser}}
\newcommand\rosserlifetime  {(1907--1989)}
\newcommand\rousseau        {{\namefont Rousseau}}
\newcommand\rousseauname    {{\namefont \jean-\jacques\ \rousseau}}
\newcommand\rousseaulifetime{(1712--1778)}
% Jean Rubin:  Oct. 29, 1926 -- Oct. 25, 2002
% Herman Rubin:  Oct. 27, 1926 and as far as I know Herman is still living and
% teaching at Purdue. info by Paul Howard
\newcommand\rubinheindex                 {\index{Rubin, Herman  (*1926)}} 
\newcommand\protectedrubinheindex{\protect\index{Rubin, Herman  (*1926)}} 
\newcommand\rubinsheindex                 {\index{Rubin, Jean E. (1926--2002)}} 
\newcommand\protectedrubinsheindex{\protect\index{Rubin, Jean E. (1926--2002)}} 
\newcommand\rubin           {Rubin}
\newcommand\rubinhename     {Herman \rubin}
\newcommand\rubinshename    {\jean\ E. \rubin}
\newcommand\rusinowitch     {Rusino\-witch}
\newcommand\rusinowitchname {\michael\ \rusinowitch}
\newcommand\russellindex                 {\index{Russell, Bertrand (1872--1970)}}
\newcommand\protectedrussellindex{\protect\index{Russell, Bertrand (1872--1970)}}
\newcommand\russellsparadoxindex{\index{Russell's Paradox}}
\newcommand\russell         {{\namefont Russell}}
\newcommand\russellname     {\russellindex{\namefont Bertrand \russell}}
% {Bertrand A.\,W. \russell} % no space after A.
\newcommand\russelllifetime {(1872--1970)}
\newcommand\russellsparadox {\russellsparadoxindex\russell'\es\ Paradox}
\newcommand\sankappanavar   {Sankappanavar}
\newcommand\sankappanavarname{H. P. \sankappanavar}
\newcommand\sannella        {Sannella}
\newcommand\sannellaname    {\donald\ T. \sannella}
\newcommand\salzer          {{\namefont Salzer}}
\newcommand\salzername      {{\namefont Gernot \salzer}}
\newcommand\sartreindex     {\index{Sartre, Jean Paul (1905--1980)}}
\newcommand\sartre          {{\namefont Sartre}}
\newcommand\sartrename      {\sartreindex{\namefont\jean\ \paul\ \sartre}}
\newcommand\sartrelifetime  {(1905--1980)}
\newcommand\sattler         {{\namefont Sattler-Klein}}
\newcommand\sattlername     {{\namefont Andrea \sattler}}
\newcommand\samoaindex      {\index{Schmidt-Samoa, Tobias (*1973)}}
\newcommand\protectedsamoaindex{\protect\index{Schmidt-Samoa, Tobias (*1973)}}
\newcommand\samoa           {{\namefont Schmidt-Sa\-moa}}
\newcommand\samoaname       {\samoaindex{\namefont\tobias\ \samoa}}
\newcommand\samoalifetime   {(*1973)}
\newcommand\scanlonindex    {\index{Scanlon, Thomas M., Jr. (*1940)}}
\newcommand\protectedscanlonindex
                    {\protect\index{Scanlon, Thomas M., Jr. (*1940)}}
\newcommand\scanlon         {{\namefont Scanlon}}
\newcommand\scanlonname     {\scanlonindex{\namefont\thomas\ M. \scanlon\ \jr}}
\newcommand\scanlonlifetime {(*1940)}
\newcommand\schaperindex    {\index{Schaper, Hans von}}
\newcommand\schaper         {{\namefont Schaper}}
\newcommand\schapername     {\schaperindex{\namefont\hans\ von \schaper}}
\newcommand\schiller        {{\namefont Schiller}}
\newcommand\schillername    {{\namefont\friedrich\ von \schiller}}
\newcommand\schillermarvinindex{\index{Schiller, Marvin (*1979)}}
\newcommand\schillermarvinname{\schillermarvinindex{\namefont\marvin\ \schiller}}
\newcommand\schillermarvinlifetime{(*1979)}
\newcommand\schlick         {{\namefont Schlick}}
\newcommand\schlickname     {{\namefont Moritz \schlick}}
\newcommand\schlicklifetime {(1882--1936)}
\newcommand\schmidt         {{\namefont Schmidt}}
\newcommand\fkschmidtname   {{\namefont\friedrich\ \karl\ \schmidt}}
\newcommand\arnoldschmidtname{{\namefont H. \hskip-.2em Ar\-nold \schmidt}}
\newcommand\schmitt         {{\namefont Schmitt}}
\newcommand\schmittname     {{\namefont\peter\ H. \schmitt}}
\newcommand\schneiderindex  {\index{Schneider, Hubert H. (1926--1990)}}
\newcommand\schneider       {{\namefont Schneider}}
\newcommand\schneidername   {\schneiderindex{\namefont\hubert\ H. \schneider}}
\newcommand\schneiderlifetime{(1926--1990)}
\newcommand\schoenfinkelindex
                      {\index{Schoenfinkel@Sch\oe n\-finkel, Moses (1889--1942)}}
\newcommand\schoenfinkel    {{\namefont Sch\oe n\-finkel}}
\newcommand\schoenfinkelname
                           {\schoenfinkelindex{\namefont Mose\es\ \schoenfinkel}}
\newcommand\schoenfinkellifetime{(1889--1942)}
\newcommand\scholzindex     {\index{Scholz, Heinrich (1884--1956)}}
\newcommand\scholz          {{\namefont Scholz}}
\newcommand\scholzname      {\scholzindex{\namefont\heinrich\ \scholz}}
\newcommand\scholzlifetime  {(1884--1956)}
\newcommand\schroederindex  {\index{Schroeder@Schr\"oder, Ernst (1841--1902)}}
\newcommand\protectedschroederindex
                    {\protect\index{Schroeder@Schr\"oder, Ernst (1841--1902)}}
\newcommand\schroeder       {{\namefont Schr\oe der}}
\newcommand\schroedername   {\schroederindex{\namefont\ernst\ \schroeder}}
\newcommand\schroederlifetime{(1841--1902)}
\newcommand\schroedinger    {Schr\oe\-din\-ger}
\newcommand\schuermann      {{\namefont Sch\ue r\-mann}}
\newcommand\schuermannname  {{\namefont\carsten\ \schuermann}}
\newcommand\schuetteindex   {\index{Schuette@Sch\"utte, Kurt (1909--1998)}}
\newcommand\protectedschuetteindex
                         {\protect\index{Schuette@Sch\"utte, Kurt (1909--1998)}}
\newcommand\schuette        {{\namefont Sch\ue tte}}
\newcommand\schuettename    {\schuetteindex{\namefont\kurt\ \schuette}}
\newcommand\schuettelifetime{(1909--1998)}
\newcommand\schulz          {Schulz}
\newcommand\schulzname      {\stephan\ \schulz}
\newcommand\schwaller       {{\namefont Schwaller de Lubicz}}
\newcommand\schwallername   {{\namefont \rene\ A. \schwaller}}
\newcommand\schwallerlifetime{(1887--1961)}
\newcommand\schweitzer      {{\namefont Schweitzer}}
\newcommand\schweitzername  {{\namefont\albert\ \schweitzer}}
\newcommand\schweitzerlifetime{(1875--1965)}
\newcommand\schweizer       {{\namefont Schweizer}}
\newcommand\schweizername   {{\namefont\stephan\ \schweizer}}
\newcommand\schwichtenberg  {{\namefont Schwichten\-berg}}
\newcommand\schwichtenbergname{{\namefont\helmut\ \schwichtenberg}}
\newcommand\scottindex      {\index{Scott, Dana S. (*1932)}}
\newcommand\protectedscottindex{\protect\index{Scott, Dana S. (*1932)}}
\newcommand\scott           {{\namefont Scott}}
\newcommand\scottname       {\scottindex{\namefont Dana S. \scott}}
\newcommand\scottlifetime   {(*1932)}
\newcommand\sengler         {{\namefont Sengler}}
\newcommand\senglername     {{\namefont\claus\ \sengler}}
\newcommand\shakespeare     {Shakespeare}
\newcommand\shakespearename {\william\ \shakespeare}
\newcommand\shan            {{\namefont Shan}}
\newcommand\shanname        {{\namefont Chung-chieh \shan}}
\newcommand\shankarindex    {\index{Shankar, Natarajan}}
\newcommand\protectedshankarindex{\protect\index{Shankar, Natarajan}}
\newcommand\shankar         {{\namefont Shankar}}
\newcommand\shankarname     {\shankarindex{\namefont Natarajan \shankar}}
\newcommand\sheffer         {{\namefont Sheffer}}
\newcommand\shefferindex    {\index{Sheffer, Henry Maurice (1882--1964)}}
\newcommand\shefferstrokeindex{\index{Sheffer stroke}}
\newcommand\sheffername     {\shefferindex{\namefont\henry\ \maurice\ \sheffer}}
\newcommand\shefferstrokenamenoindex{\sheffer\ stroke}
\newcommand\shefferstrokename{\shefferstrokeindex\shefferstrokenamenoindex}
\newcommand\shefferlifetime {(1882--1964)}
\newcommand\shoenfieldindex {\index{Shoenfield, Joseph R. (1927--2000)}}
\newcommand\protectedshoenfieldindex
                    {\protect\index{Shoenfield, Joseph R. (1927--2000)}}
\newcommand\shoenfield      {{\namefont Shoenfield}}
\newcommand\shoenfieldname  {\shoenfieldindex{\namefont\joseph\ R. \shoenfield}}
\newcommand\shoenfieldlifetime{(1927--2000)}
\newcommand\siefkes         {{\namefont Siefkes}}
\newcommand\siefkesname     {{\namefont\dirk\ \siefkes}}
\newcommand\siegindex       {\index{Sieg, Wilfried}}
\newcommand\sieg            {{\namefont Sieg}}
\newcommand\siegname        {\siegindex{\namefont\wilfried\ \sieg}}
\newcommand\siekmannindex   {\index{Siekmann, \joerg\ (*1941)}}
\newcommand\siekmann        {{\namefont Siek\-mann}}
\newcommand\siekmannname    {\siekmannindex{\namefont \joerg\ \siekmann}}
% The true name is actually \hans-\joerg\ \siekmann.
% Thus, the often found \joerg\ H. \siekmann\ is rubbish.
\newcommand\siekmannlifetime{(*1941)}
\newcommand\simariindex     {\index{Simari, Guillermo R.}}
\newcommand\simari          {{\namefont Simari}}
\newcommand\simariname      {\simariindex{\namefont Guillermo R. \simari}}
\newcommand\simonyiindex    {\index{Simonyi, Charles}}
\newcommand\simonyi         {{\namefont Simonyi}}
\newcommand\simonyiname     {\simonyiindex{\namefont\charles\ \simonyi}}
\newcommand\simonyilifetime {(*1948)}
\newcommand\simpson         {{\namefont Simpson}}
\newcommand\simpsonname     {{\namefont Alex \simpson}}
\newcommand\sivakumarname   {{\namefont G. Sivakumar}}
\newcommand\skolemindex     {\index{Skolem, Thoralf (1887--1963)}}
\newcommand\protectedskolemindex{\protect\index{Skolem, Thoralf (1887--1963)}}
\newcommand\skolem          {{\namefont Skolem}}
\newcommand\skolemname      {\skolemindex\thoralf\ % A.
                             \skolem}
\newcommand\skolemlifetime  {(1887--1963)}
\newcommand\skolemizing     {\skolem\-izing}
\newcommand\skolemization   {\skolem\-ization}
\newcommand\skolemizedform  {\skolem\-ized form}   
\newcommand\skolemizedForm  {\skolem\-ized Form}   
% for validity, this is
% to denote the form that results by getting all general (universal) 
% quantifiers to the top on the price of incrementing their order,
% as used in Loewenheim (1915) and Skolem (1928).
\newcommand\skolemnormalform
{\index{Skolem normal form}\skolem\ normal form}% for validity, this is 
% to denote the form that results by getting all restricted (existential)
% quantifiers to the top on the price of adding new relation symbols for the
% subformulas starting with general quantification
\newcommand\skolemsparadox  {\index{Skolem's Paradox}\skolem's Paradox}
\newcommand\slind           {{\namefont Slind}}
\newcommand\slindname       {{\namefont\konrad\ \slind}}
\newcommand\smaill          {{\namefont Smaill}}
\newcommand\smaillname      {{\namefont\alan\ \smaill}}
\newcommand\smith           {{\namefont Smith}}
\newcommand\smithname       {{\namefont\james\ T. \smith}}
\newcommand\smolka          {{\namefont Smolka}}
\newcommand\smolkaname      {{\namefont Gert \smolka}}
\newcommand\smullyan        {{\namefont Smullyan}}
\newcommand\smullyanname    {{\namefont\raymond\ M. \smullyan}}
\newcommand\smullyanlifetime{(*1919)}
\newcommand\snyder          {Snyder}
\newcommand\snydername      {Wayne \snyder}
\newcommand\sobocinskiindex 
                     {\index{Sobociinski@Soboci\'nski, Boles\l aw (1906--1990)}}
\newcommand\sobocinski      {{\namefont Soboci\'nski}}
\newcommand\sobocinskiname  {\sobocinskiindex{\namefont Boles\l aw \sobocinski}}
\newcommand\sobocinskilifetime{(1906--1990)}
\newcommand\sokrates        {{\namefont Sokrates}}
\newcommand\sokratesname    {{\namefont \sokrates\ the Older}}
\newcommand\sokrateslifetime{(469--399\BC)}
\newcommand\solon           {{\namefont Solon}}
\newcommand\solonname       {{\namefont \solon}}
\newcommand\solonlifetime   {(638?--after\,561\BC)}
\newcommand\spohn           {{\namefont Spohn}}
\newcommand\spohnname       {{\namefont\wolfgang\ \spohn}}
\newcommand\sprenger        {Spren\-ger}
\newcommand\sprengername    {Christof \sprenger}
\newcommand\spurr           {{\namefont Spurr}}
\newcommand\spurrname       {{\namefont Jane \spurr}}
\newcommand\stanisfer       {{\namefont Stanisfer}}
\newcommand\stanisfername   {{\namefont Ryan \stanisfer}}
\newcommand\staples         {Staple\es}
\newcommand\staplesname     {\john\ \staples}
\newcommand\steele          {Steele}
\newcommand\steelename      {Guy L. \steele\ \jr}
\newcommand\steffenname     {\bernhard\ Steffen}
\newcommand\steinbach       {{\namefont Steinbach}}
\newcommand\steinbachname   {{\namefont\joachim\ \steinbach}}
\newcommand\stephansecondname{{\namefont Stephan}}
\newcommand\stephansecondnamename{{\namefont\werner\ \stephansecondname}}
\newcommand\stevens         {{\namefont Steven\es}}
\newcommand\stevensname     {{\namefont\andrew\ \stevens}}
\newcommand\stickel         {Stickel}
\newcommand\stickelname     {Mark E. \stickel}
\newcommand\Stoic           {{\namefont Stoic}}
\newcommand\StoicMegarian   {{\namefont\Stoic--Megarian}}
\newcommand\stolzenburg     {{\namefont Stol\-zen\-burg}}
\newcommand\stolzenburgname {{\namefont Frie\-der \stolzenburg}}
\newcommand\stratulat       {Stratulat}
\newcommand\stratulatname   {Sorin \stratulat}
\newcommand\stuber          {Stu\-ber}
\newcommand\stubername      {\juergen\ \stuber}
\newcommand\suppesindex     {\index{Suppes, Patrick (*1922)}}
\newcommand\suppes          {{\namefont Suppes}}
\newcommand\suppesname      {\suppesindex{\namefont Patrick \suppes}}
\newcommand\suppeslifetime  {(*1922)}
\newcommand\sutcliffe       {Sutcliffe}
\newcommand\sutcliffename   {Geoff \sutcliffe}
\newcommand\suzuki          {Suzuki}
\newcommand\suzukiname      {Taro \suzuki}
\newcommand\szabo           {{\namefont Szabo}}
\newcommand\szaboname       {{\namefont \manfred\ E. \szabo}}
\newcommand\taitindex                 {\index{Tait, William W. (*1929)}}
\newcommand\protectedtaitindex{\protect\index{Tait, William W. (*1929)}}
\newcommand\tait            {{\namefont Tait}}
\newcommand\taitname        {\taitindex{\namefont William W. \tait}}
\newcommand\taitlifetime    {(*1929)}
\newcommand\takagi          {{\namefont Takagi}}
\newcommand\takaginame      {{\namefont Teiji \takagi}}
\newcommand\takagilifetime  {(1875--1960)}
\newcommand\takeutiindex    {\index{Takeuti, Gaisi (*1926)}}
\newcommand\takeuti         {{\namefont Takeuti}}
\newcommand\takeutiname     {\takeutiindex{\namefont Gaisi \takeuti}}
\newcommand\takeutilifetime {(*1926)}
\newcommand\tanneryindex    {\index{Tannery, Paul (1843--1904)}}
\newcommand\tannery         {{\namefont Tannery}}
\newcommand\tanneryname     {{\namefont \paul\ \tannery}}
\newcommand\tannerylifetime {(1843--1904)}
\newcommand\tappindex       {\index{Tapp, Christian}}
\newcommand\tapp            {{\namefont Tapp}}
\newcommand\tappname        {\tappindex{\namefont\christian\ \tapp}}
\newcommand\tarskiindex                 {\index{Tarski, Alfred (1901--1983)}}
\newcommand\protectedtarskiindex{\protect\index{Tarski, Alfred (1901--1983)}}
\newcommand\tarski          {{\namefont Tar\-ski}}
\newcommand\tarskiname      {\tarskiindex{\namefont\alfred\ \tarski}}
\newcommand\tarskilifetime  {(1901--1983)}
\newcommand\tarskigrothendieck{\tarski--\grothendieck}
\newcommand\thomasaquinas   {{\namefont\thomas}}
\newcommand\thomasaquinasname{{\namefont\thomasaquinas\ Aquina\es}}
\newcommand\thomasaquinaslifetime{(1225?--1274)}
\newcommand\thales          {{\namefont Thales}}
\newcommand\theiss          {{\namefont Theiss}}
\newcommand\theissname      {{\namefont\frank\ \theiss}}
\newcommand\thimm           {{\namefont Thimm}}
\newcommand\thimmname       {{\namefont\matthias\ \thimm}}
\newcommand\thurber         {{\namefont Thurber}}
\newcommand\thurbername     {{\namefont\james\ \thurber}}
\newcommand\toepell         {{\namefont Toepell}}
\newcommand\toepellname     {{\namefont\michaelwithouttrema-\markus\ \toepell}}
\newcommand\torrettiindex   {\index{Torretti, Roberto (*1930)}}
\newcommand\torretti        {{\namefont Torretti}}
\newcommand\torrettiname    {\torrettiindex{\namefont Roberto \torretti}}
\newcommand\torrettilifetime{(*1930)}
\newcommand\toyama          {{\namefont Toyama}}
\newcommand\toyamaname      {{\namefont Yoshihito \toyama}}
\newcommand\troelstra       {{\namefont Troelstra}}
\newcommand\troelstraname   {{\namefont\anne\ Sjerp \troelstra}}
%                           {{\namefont\anne\ S. \troelstra}}
\newcommand\trotzki         {{\namefont Trotsky}}
\newcommand\trotzkiname     {{\namefont Leon \trotzki}}
\newcommand\trotzkilifetime {(1879--1940)}
\newcommand\turingindex     {\index{Turing, Alan (1912--1954)}}
\newcommand\turing          {{\namefont Turing}}
\newcommand\turingname      {{\namefont\alan\ \turing}}
\newcommand\turinglifetime  {(1912--1954)}
\newcommand\ulrici          {{\namefont Ulrici}}
\newcommand\ulriciname      {{\namefont\hermann\ \ulrici}}
\newcommand\ulricilifetime  {(1806--1884)}
\newcommand\unguru          {{\namefont Unguru}}
\newcommand\unguruname      {{\namefont Sabetai \unguru}}
\newcommand\unruhindex      {\index{Unruh, Fritz von (1885--1970)}}
\newcommand\unruh           {{\namefont Unruh}}
\newcommand\unruhname       {\unruhindex{\namefont Fritz von \unruh}}
\newcommand\unruhlifetime   {(1885--1970)}
\newcommand\unverzagt       {{\namefont Unverzagt}}
\newcommand\stephanunverzagtname{{\namefont \stephan\ \unverzagt}}
\newcommand\urysohn         {{\namefont Urysohn}}
\newcommand\urysohnname     {{\namefont Pavel Samuilovich \urysohn}}
\newcommand\urysohnlifetime {(1898--1924)}

\newcommand\vaihingerindex  {\index{Vaihinger, Hans (1852--1933)}} 
\newcommand\vaihinger       {{\namefont Vaihinger}}
\newcommand\vaihingername   {\vaihingerindex{\namefont\hans\ \vaihinger}}
\newcommand\vaihingerlifetime{(1852--1933)} 
\newcommand\vandeveire      {Van de Veire}
\newcommand\vandeveirename  {Ann \vandeveire}
\newcommand\veblenindex                 {\index{Veblen, Oswald (1880--1960)}}
\newcommand\protectedveblenindex{\protect\index{Veblen, Oswald (1880--1960)}}
\newcommand\veblen          {{\namefont Veblen}}
\newcommand\veblenname      {\veblenindex{\namefont Oswald \veblen}}
\newcommand\veblenlifetime  {(1880--1960)}
\newcommand\venn            {Venn}
\newcommand\vennname        {\john\ \venn}
\newcommand\vennlifetime    {(1834--1923)}
\newcommand\venndiagram     {\venn\ diagram}
\newcommand\vessiotindex    {\index{Vessiot, Ernest (1865--1952)}} 
\newcommand\vessiot         {{\namefont Vessiot}}
\newcommand\vessiotname     {\vessiotindex{\namefont\ernest\ \vessiot}}
\newcommand\vessiotlifetime {(1865--1952)}
\newcommand\viete           {{\namefont Vi\`ete}}
\newcommand\vietename       {{\namefont\francois\ \viete}}
\newcommand\vietelifetime   {(1540--1603)}
\newcommand\villon          {Villon}
\newcommand\villonname      {\francois\ \villon}
\newcommand\voigtindex      {\index{Voigt, Andreas Heinrich (1860--1940)}}
\newcommand\voigt           {{\namefont Voigt}}
\newcommand\voigtname       {\voigtindex{\namefont\andreas\ \heinrich\ \voigt}}
\newcommand\voigtlifetime   {(1860--1940)}
\newcommand\voronkov        {{\namefont Voron\-kov}}
\newcommand\voronkovname    {{\namefont Andrei \voronkov}}
\newcommand\wagnerindex     {\index{Wagner, Marc (*1981)}}
\newcommand\wagner          {{\namefont Wag\-ner}}
\newcommand\wagnername      {\wagnerindex{\namefont Marc \wagner}}
\newcommand\waerdenindex  {\index{Waerden, Bartel Leendert van der (1903--1996)}}
\newcommand\waerden         {{\namefont Waerden}}
\newcommand\waerdenname
                      {\waerdenindex{\namefont Bartel Leendert van der \waerden}}
\newcommand\waerdenlifetime {(1903--1996)}
\newcommand\wajsbergindex{\index{Wajsberg@Waj\esi berg, Mordechai (1902--1940?)}}
\newcommand\wajsberg        {{\namefont Waj\esi berg}}
\newcommand\wajsbergname    {\wajsbergindex{\namefont Morde\-chai \wajsberg}}
\newcommand\wajsberglifetime{(1902--1940?)}
\newcommand\waldmann        {Wald\-mann}
\newcommand\waldmanneinsname{\bernard\ \waldmann}
\newcommand\waldmannzweiname{\uwe\ \waldmann}
\newcommand\wallen          {{\namefont Wallen}}
\newcommand\wallenname      {{\namefont Lincoln A. \wallen}}
\newcommand\walsh           {{\namefont Walsh}}
\newcommand\walshname       {{\namefont Toby \walsh}}
\newcommand\walshtwoname    {C. M. \walsh}
\newcommand\walters         {Walter\es}
\newcommand\waltersname     {Humphrey \robert\ ``Pum'' \walters}
\newcommand\waltherindex    {\index{Walther, Christoph (*1950)}}
\newcommand\protectedwaltherindex{\protect\index{Walther, Christoph (*1950)}}
\newcommand\walther         {{\namefont Walther}}
\newcommand\walthername     {\waltherindex{\namefont\christoph\ \walther}} 
\newcommand\waltherlifetime {(*1950)}
\newcommand\wangindex                 {\index{Wang, Hao (1921--1995)}}
\newcommand\protectedwangindex{\protect\index{Wang, Hao (1921--1995)}}
\newcommand\wang            {{\namefont Wang}} 
\newcommand\wangname        {\wangindex{\naemfont Hao \wang}} 
\newcommand\wanglifetime    {(1921--1995)}
\newcommand\waringindex     {\index{Waring, Edward (1736(?)--1798)}}
\newcommand\waring          {{\namefont Waring}}
\newcommand\waringname      {\waringindex{\namefont\edward\ \waring}}
\newcommand\waringlifetime  {(1736(?)--1798)}
\newcommand\wahringsproblemindex{\index{Waring's Problem}}
\newcommand\waringsproblem  {\wahringsproblemindex\waring's Problem}
\newcommand\waringschesproblem{\wahringsproblemindex\waring sches Problem}
\newcommand\wedderburnindex {\index{Wedderburn, J. H. M. (1882--1948)}}
\newcommand\wedderburn      {{\namefont Wedderburn}}
\newcommand\wedderburnname  {\wedderburnindex{\namefont J. H. M. \wedderburn}}
% This is the way Wedderburn signed his letter to Hasse
% Joseph is prominent on Wikipedia. Maclagen is how Herbrand called him.
%                           {{\namefont\joseph\ \henry\ Maclagen \wedderburn}}
\newcommand\wedderburnlifetime{(1882--1948)}
\newcommand\weberindex      {\index{Weber, Heinrich (1842--1913)}}
\newcommand\weber           {{\namefont Weber}}
\newcommand\webername       {\weberindex{\namefont \heinrich\ \weber}}
\newcommand\weberlifetime   {(1842--1913)}
\newcommand\wegener         {Wegener} 
\newcommand\wegenername     {Ingo \wegener} 
\newcommand\wegman          {Wegman} 
\newcommand\wegmanname      {Mark N. \wegman} 
\newcommand\weidenbach      {{\namefont Weidenbach}}
\newcommand\weidenbachname  {{\namefont\christoph\ \weidenbach}}
\newcommand\weierstrassindex{\index{Weierstrass@Weierstra\sz, Karl (1815--1897)}}
\newcommand\weierstrass     {{\namefont Weierstra\sz}}
% \newcommand\weierstrassnosz {{\namefont Weierstra\ses}}
\newcommand\weierstrassname {\weierstrassindex{\namefont\karl\ \weierstrass}}
\newcommand\weierstrasslifetime{(1815--1897)}
\newcommand\weilindex       {\index{Weil, Andr\'e (1906--1998)}}
\newcommand\weil            {{\namefont Weil}}
\newcommand\weilname        {\weilindex{\namefont Andr\'e \weil}}
\newcommand\weillifetime    {(1906--1998)}
\newcommand\wertheimer      {Wertheimer}
\newcommand\wertheimername  {\maxchristianname\ \wertheimer}
\newcommand\wertheimerlifetime{(1880--1943)}
\newcommand\weylindex       {\index{Weyl, Hermann (1885--1955)}}
\newcommand\protectedweylindex{\protect\index{Weyl, Hermann (1885--1955)}}
\newcommand\weyl            {{\namefont Weyl}}
\newcommand\weylname        {\weylindex{\namefont\hermann\ \weyl}}
\newcommand\weyllifetime    {(1885--1955)}
\newcommand\whitesurname    {{\namefont White}}
\newcommand\whitename       {{\namefont Roger M. \whitesurname}} 
\newcommand\whitelifetime   {(*1938)}
\newcommand\whiteheadindex  {\index{Whitehead, Alfred North (1861--1947)}}
\newcommand\whitehead       {{\namefont White\-head}}
\newcommand\whiteheadname   {\whiteheadindex{\namefont\alfred\ North \whitehead}}
\newcommand\whiteheadlifetime{(1861--1947)}
\newcommand\PM              {Principia Mathematica}
\newcommand\PMshort         {Principia}
\newcommand\principleofdependentchoice{\principleofdependentchoiceindex
                                                  Principle of Dependent Choice}
\newcommand\principleofdependentchoiceindex{\index
{choice!Principle of Dependent Choice}}
\newcommand\principleofdependentchoiceindexsee{\index
{Principle of Dependent Choice|see{choice, Principle of Dependent Choice}}}%
\newcommand\wiles           {{\namefont Wiles}}
\newcommand\wilesname       {{\namefont\andrew\ \wiles}}
\newcommand\wilhelmname     {{\namefont Rein\-hard \wilhelm}}
\newcommand\wirthindex                 {\index{Wirth, Claus-Peter (*1963)}}
\newcommand\protectedwirthindex{\protect\index{Wirth, Claus-Peter (*1963)}}
\newcommand\wirth           {{\namefont Wirth}}
\newcommand\wirthnamenoindex{{\namefont\claus-\peter\ \wirth}}
\newcommand\wirthname       {\wirthindex\wirthnamenoindex}
\newcommand\wirthlifetime   {(*1963)}
\newcommand\ellinorwirthname{{\namefont Ellinor \wirth}}
\newcommand\arianawirthname {{\namefont Ariana \wirth}}
\newcommand\wirtz           {{\namefont Wirtz}}
\newcommand\wirtzname       {{\namefont Daniela \wirtz}}
\newcommand\wittgensteinindex{\index{Wittgenstein, Ludwig (1889--1951)}}
\newcommand\protectedwittgensteinindex{\protect
                              \index{Wittgenstein, Ludwig (1889--1951)}}
\newcommand\wittgenstein    {{\namefont Wittgenstein}} 
\newcommand\wittgensteinname{\wittgensteinindex{\namefont\ludwig\ \wittgenstein}}
\newcommand\wittgensteinlifetime{(1889--1951)}
\newcommand\wittgensteinproject
                           {{\namefont\wittgenstein\ ``Vienna Edition'' Project}}
\newcommand\wolff           {{\namefont Wolff}} 
\newcommand\wolffname       {{\namefont\christian\ \wolff}} 
%                           {{\namefont\christian\ Freiherr von \wolff}} 
\newcommand\wolfflifetime   {(1679--1754)}
\newcommand\wolskaindex     {\index{Wolska, Magdalena (*1973)}}
\newcommand\wolska          {{\namefont Wol\-ska}}
\newcommand\wolskaname      {\wolskaindex{\namefont\magdalena\ \wolska}}
%                           {{\namefont\magdalena\ A. M. \wolska}}
\newcommand\woods           {{\namefont Wood\es}}
\newcommand\woodsname       {{\namefont\john\ \woods}}
\newcommand\woudename       {Jaap van der Woude}
\newcommand\wrightghindex   {\index{Wright, Georg Henrik (1916--2003)}}
\newcommand\wright          {\mbox{\namefont Wright}}
\newcommand\wrightghname    {{\namefont\georg\ \henrik\ von \wright}}
\newcommand\wrightlifetime  {(1916--2003)}
\newcommand\wrightson       {{\namefont Wright\-son}}
\newcommand\wrightsonname   {{\namefont Graham \wrightson}}
\newcommand\yamada          {Yamada}
\newcommand\yamadaname      {Toshiyuki \yamada}
\newcommand\zachindex       {\index{Zach, Richard}}
\newcommand\zach            {{\namefont Zach}}
\newcommand\zachname        {\zachindex{\namefont\richard\ \zach}}
\newcommand\zantema         {{\namefont Zantema}}
\newcommand\zantemaname     {{\namefont\hans\ \zantema}}
\newcommand\zarembaindex    {\index{Zaremba, Stanis{\l}aw (1863--1942)}}
\newcommand\protectedzarembaindex{\protect
                             \index{Zaremba, Stanis{\l}aw (1863--1942)}}
\newcommand\zaremba         {{\namefont Zaremba}}
\newcommand\zarembaname     {\zarembaindex{\namefont\stanislaw\ \zaremba}}
\newcommand\zarembalifetime {(1863--1942)}
\newcommand\zeno            {{\namefont Zeno}} 
\newcommand\zenoeinsindex   
       {\index{Zeno of Elea@Zeno of Elea (\protect\nth 5\,century\,\BC)}}
\newcommand\zenoeinsname    {\zenoeinsindex{\namefont \zeno\ of Elea}}
                           % elatic school
\newcommand\zenoeinslifetime{(\nth 5\,century\,\BC)}
% The following is obsolete, because non-standard in English. 
% Use \achillesparadox instead.
%\newcommand\zenosparadoxindex{\index{Zeno!'s Achilles Paradox}}
%\newcommand\zenosparadox
% {\achillesparadoxindex\zenosparadoxindex{\zeno's {\namefont\achilles} Paradox}}
%                           % the paradox stems from \zenoeinsname 
\newcommand\achillesparadoxindex{\index{Achilles Paradox}}
\newcommand\achillesparadox{\achillesparadoxindex{{\namefont\achilles} Paradox}}
% The Achilles Paradox stems from \zenoeinsname\ and shows that if space is a
% continuum and there is no infinity, then Achilles cannot overtake the tortoise.
\newcommand\stadiumparadoxindex{\index{Stadium Paradox}}
\newcommand\stadiumparadox{\stadiumparadoxindex{Stadium Paradox}}
% The Stadium Paradox stems from \zenoeinsname\ and shows that if space is not
% continuous, two, say three atomic units long, objects moving in opposite 
% direction with identical speed, say in a straight running track in a stadium, 
% never get a to a position where the two 
% first units of the one line up with the two first of the other, or
% never line up perfectly in the middle,
% or one moves twice as fast as the other,
% or we get to the hardest form the Arrow Paradox.
% Start position: 
% LLL
%   RRR
% Potential immediate follow-up position:
%  LLL
%  RRR
% Here the relative position of LLL
%                                RRR
% does never occur.
% Alternative immediate follow-up position:
% LLL
%  RRR
% Possible Second Follow-up:
%  LLL
% RRR
% In this case RRR moves twice as fast as LLL.
% Alternative Second Follow-up:
%  LLL
%  RRR
% This case is actuall treated in the Arrow Paradox
% because RRR rests two units of time at the same place.
\newcommand\arrowparadoxindex{\index{Arrow Paradox}}
\newcommand\arrowparadox{\arrowparadoxindex{Arrow Paradox}}
                           % the paradox stems from \zenoeinsname 
\newcommand\zenozweiname    {{\namefont \zeno\ of Citium}}
                           % founder of stoic school
\newcommand\zenozweilifetime{(\ca\,333--262\,\BC)}
\newcommand\zenodreiname    {{\namefont \zeno\ of Sidon}}
                           % Epicurean school, induction
\newcommand\zenodreilifetime{(\ca\,150--70\,\BC)}
\newcommand\zermeloindex    {\index{Zermelo, Ernst (1871--1953)}}
\newcommand\protectedzermeloindex{\protect\index{Zermelo, Ernst (1871--1953)}}
\newcommand\zermelo         {{\namefont Zermelo}}
\newcommand\zermeloname     {\zermeloindex{\namefont \ernst\ \zermelo}}
%                           {{\namefont \ernst\ F. E. \zermelo}}
\newcommand\zermelolifetime {(1871--1953)}
\newcommand\ZFlong          {\zermelo--\fraenkel}
\newcommand\ZFshort         {{\sc ZF}}
\newcommand\zhang           {{\namefont Zhang}}
\newcommand\zhangname       {{\namefont Han\-tao \zhang}}
\newcommand\zorn            {{\namefont Zorn}} 
\newcommand\zuse            {{\namefont Zuse}}
\newcommand\zusename        {{\namefont\konrad\ \zuse}}
%                           {{\namefont\konrad\ E. O. \zuse}}
\newcommand\zuselifetime    {(1910--1995)}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ABBREVIATIONS and SPECIAL WORDS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%General:

\newcommand\am   {a.m.}
\newcommand\ASF  {ASF}
\newcommand\asfplus{\ASF\/\math{^+}}
\newcommand\afortiori{a fortiori}
\newcommand\Afortiori{A fortiori}
%\newcommand\Av   {\mbox{{A}\hspace{-.09em}{v}}}
\newcommand\appendixes{appendixes}
\newcommand\Apr  {April}
\newcommand\atall{at \nolinebreak all}
\newcommand\Aug  {Aug.}
\newcommand\ca   {ca.}
\newcommand\Ca   {Ca.}
\newcommand\ct   {c.t.}
\newcommand\fiance{fianc\'e}
\newcommand\FB   {FB}
\newcommand\FBinf{Fachbereich Informatik}
\newcommand\FBinfshort{\FB\ Informatik}
\newcommand\FBautinfshort{\FB\ Automatisierung und Informatik}
\newcommand\FBautinfveryshort{\FB\ AI}
\newcommand\FR   {FR}
\newcommand\FRinf{Fachrichtung Informatik}
\newcommand\FRinfshort{\FR\ Informatik}
\newcommand\f    {\mbox{}{f.}}   %extra block blocks ligature to VI\f
\newcommand\ff   {\mbox{}{ff.}}  %extra block blocks ligature to VI\ff
\newcommand\Fa   {Fa.} % Modis
\newcommand\Feb  {Feb.}
\newcommand\FreeVariable{Free-\math\!Variable}
\newcommand\freevariable{free-variable}
\newcommand\freely{free}
\newcommand\defi {Definition} % note that this controls \litdefiref and \defiref
\newcommand\Dr   {Dr.}
\newcommand\Drrernat{Dr.\,\,rer.\,\,nat.}
\newcommand\EMAIL{E-mail}
\newcommand\eMAIL{e-mail}
\newcommand\ifandonlyif{if \nolinebreak and \onlyif}
\newcommand\Int  {Int.}
\newcommand\international{int.} % \int is the integral in math mode
\newcommand\Inc  {Inc.}
\newcommand\Inst {Inst.}
\newcommand\Jan  {Jan.}
\newcommand\jr   {Jr.}
\newcommand\Math {Math.}
\newcommand\mathe{math.}
\newcommand\MASlong{Mathematics Assistance System}
\newcommand\Maslong{Mathematics assistance system}
\newcommand\maslong{mathematics assistance system}
\newcommand\naiv {na\iwithtrema v}
\newcommand\naive{na\iwithtrema ve}
\newcommand\Naive{Na\iwithtrema ve}
\newcommand\Numero{No.}
\newcommand\Nov  {Nov.}
\newcommand\notonly{not \nolinebreak only}
\newcommand\onlyif{only \nolinebreak if}
\newcommand\Onlyif{Only \nolinebreak if}
\newcommand\pmabbrev{p.m.} % \pm is already a command putting a +- in math
\newcommand\Prof {Prof.}
\newcommand\programme{program}
\newcommand\Programme{Program}
\newcommand\qedabbrev{q.e.d.}
\newcommand\qedhelp[1]{Q.e.d.~({#1})}
\newcommand\getittotheright[1]  
%puts argument flush right, if necessary on fol. line
{\hfill\mbox{}\penalty 100\mbox{\ \,}\nolinebreak
\hfill\hfill\hfill\nolinebreak\mbox{#1}\ignorespaces}
\newcommand\Qed      [1]{\underline{\qedhelp{#1}}}
\newcommand\Qeddouble[1]{\underline{\underline{\qedhelp{#1}}}}
\newcommand\Qedtriple[1]{\underline{\underline{\underline{\qedhelp{#1}}}}}
\newcommand\Qedbf    [1]{\mbox{\bf\qedhelp{#1}}}
\newcommand\QED      [1]{\getittotheright{\Qed      {#1}}}
\newcommand\QEDdouble[1]{\getittotheright{\Qeddouble{#1}}}
\newcommand\QEDtriple[1]{\getittotheright{\Qedtriple{#1}}}
\newcommand\QEDbf    [1]{\getittotheright{\Qedbf    {#1}}}
\newcommand\Role{R\^ole}
\newcommand\role{r\^ole}
\newcommand\Sep  {Sept.}
\newcommand\st   {s.t.}
% s.t. = sine tempore or such that
\newcommand\Tech {Tech.}
\newcommand\Tel  {Tel.}
\newcommand\theo {Theorem}
\newcommand\uni  {Uni\-ver\-si\-t\ae t}
\newcommand\Univ {Univ.}
\newcommand\Vol  {Vol.}
\newcommand\wintersemester{WS}%{Win\-ter-Semes\-ter}
\newcommand\WWW  {WWW}
\newcommand\www  {\url{http://wirth.bplaced.net}}
\newcommand\wwwhb{\url{http://wirth.bplaced.net/p/hilbertbernays%http://www.dfki.de/hb
}}
\newcommand\urlverbraucherpreise{\url{http://www.destatis.de/jetspeed/portal/cms/Sites/destatis/Internet/DE/Content/Statistiken/Zeitreihen/WirtschaftAktuell/Preise/Content100/kpre510bv4,templateId=renderPrint.psml}}

%Abbreviations: English or Latin:

\newcommand\AI   {Artificial Intelligence}%must be capitalized!
\newcommand\asfollows{\mbox{as follows}}
\newcommand\Assoc{Assoc.}
\newcommand\aswell{as \nolinebreak well}
\newcommand\aswellas{\aswell\ \nolinebreak as}
\newcommand\BC   {{\sc b.c.}} % Cf. Lyn Dupre, Bugs in Writing, Segment 21
\newcommand\Bull {Bull.}
\newcommand\Cf   {Cf.}
\newcommand\cf   {cf.}
\def\nlbcite{\nolinebreak\cite}
\newcommand\Cfnlb{\Cf\nolinebreak}
\newcommand\cfnlb{\cf\nolinebreak}
\newcommand\Co   {Co.}
\newcommand\Comm {Comm.}
\newcommand\Comp {Comp.}
\newcommand\Conf {Conf.}
\newcommand\contd{contd.}
\newcommand\ConstructorBased{Con\-struc\-tor-Based}
\newcommand\CS   {Computer \Sci}
\newcommand\CSlong{Computer Science}
\newcommand\Dec  {Dec.}
\newcommand\Dept {Dept.}
\newcommand\descenteinfinieindex{\index{descente infinie}}
\newcommand\descenteinfinienoindex{descente infinie}
\newcommand\descenteinfinie{\descenteinfinieindex\descenteinfinienoindex}
\newcommand\Descenteinfinie{\descenteinfinieindex Descente infinie}
\newcommand\DescenteInfinie{\descenteinfinieindex Descente Infinie}
\newcommand\howdescenteinfiniegoes
{He starts with the conjecture and simplifies it by case analysis.
When he realizes that the current goal becomes 
similar to an instance of the conjecture, 
he applies the instantiated conjecture just like a lemma, 
but keeps in mind that he has actually applied an induction hypothesis. 
Finally, he searches for some \wellfounded\ ordering in which 
all the instances of the conjecture 
% he has
applied as induction hypotheses 
are smaller than the original conjecture.%
% itself.
}
\newcommand\howMethodofDescenteInfiniegoes{Show that for each 
assumed counterexample of \math\Gamma\
there is a smaller counter\-example of \math\Gamma\
\wrt\ a \wellfounded\ ordering \nlbmath<,
which does not depend on the counterexamples.}
\newcommand\theinnermostpartofW
{\math{\forall u\tight<v\stopq\app P  u}}
\newcommand\thelogicalpointofview
{At \fermat's time, natural language was still the predominant tool for 
expressing terms and equations in mathematical writing,
and it was too early for a formal axiomatization.
Moreover, note that an axiomatization captures only validity, but 
in \nolinebreak general neither induces a method of proof search
nor provides the data structures required to admit both
a formal treatment and a human-oriented proof search.
The formalizable logic part, however, of {\em\descenteinfinie}
can be expressed in what is called
the (\secondorder) {\em\theoremofnoetherianinduction} \nlbmath{(\ident{N})}, \ 
after \noethername\ \noetherlifetime. \ 
This is not to be confused with the {\em\axiomofstructuralinduction},
which is generically given for any inductively defined data structure, 
such as the {\em\axiomofstructuralinductionfirsthalf\ 
\nlbmath{(\ident{S})}
\axiomofstructuralinductionsecondhalf\ 
for the natural numbers inductively defined by the constructors
zero \nlbmath{\zeropp} and successor \nlbmath{\ssymbol}}. \
Moreover, we need the definition \nlbmath{(\Wellfpp{\tight<})}
of \wellfoundedness\ of a relation \nlbmath<\@.\smallfootroom
\par\noindent\math{\begin{array}{@{}l@{}r@{\ }l@{}}
 (\Wellfpp{\tight<}) 
&\forall Q\stopq
&\,\inparentheses{\headroom\footroom
     \exists x\stopq\app Q x
   {\nottight{\nottight{\nottight\implies}}}
     \exists m\stopq\inparentheses{\app Q m\und
     \neg\exists w\tight<m\stopq\app Q w}}
 \footroom\\\headroom
 \inpit{\ident{N}}
&\forall P\stopq
&\inparentheses{\headroom
     \forall x\stopq\app P  x
   {\nottight{\nottight{\nottight\antiimplies}}}
     \exists\tight<\stopq\inparenthesesoplist{
      \forall v\stopq\inparentheses{
           \app P  v
         \nottight{\nottight\antiimplies}
           \theinnermostpartofW}
    \oplistund
       \Wellfpp <}\!\!}
 \footroom\\\headroom
 \inpit{\ident{S}}
&\forall P\stopq
&\,\inparentheses{\headroom\forall x\stopq\app P  x
   {\nottight{\nottight{\nottight\antiimplies}}}
   \app P \zeropp\nottight\und
   \forall y\stopq\inparentheses{\app P {\spp y}\antiimplies\app P  y}}
 \footroom\\\headroom
 (\nat 1)
&\forall\boundvari x{}\stopq
&\inparentheses{
     \boundvari x{}\tightequal\zeropp
   \nottight\oder
     \exists
     \boundvari y{}\stopq
     \boundvari x{}\tightequal\spp{\boundvari y{}}}
 \footroom\\\headroom
 (\nat 2)
 &
 \forall
 \boundvari x{}\stopq
 &
 \spp x\tightnotequal\zeropp
 \footroom\\\headroom
 (\nat 3)
 &\forall x,y\stopq
 &\inparentheses{\spp x\tightequal\spp y\nottight\implies x\tightequal y}
\\\end{array}}
\par\halftop\noindent
Let \Wellfpp\ssymbol\ denote 
\Wellfpp{\lambda x,y.\,\inpit{\spp x\tightequal y}},
which implies the \wellfoundedness\ of the ordering of the natural numbers. 
The natural numbers can be specified up to isomorphism
either by \math{(\ident{S})}, \nlbmath{(\nat 2)}, 
and \nlbmath{(\nat 3)}, \hskip.15em 
or else by \Wellfpp\ssymbol\ and \nlbmath{(\nat 1)}\@.
The first alternative 
% is the traditional one, 
% following \dedekind\ and 
follows \dedekindname\ \dedekindlifetime\ and is 
named after \peanoname\ \peanolifetime. 
The second follows \pieriname\ \pierilifetime.  
As the instances for \math P and \nlbmath< in \nlbmath{\inpit{\ident{N}}}
are often still easy to find when the instances for \math P in 
\nlbmath{\inpit{\ident{S}}} are not, \hskip.15em 
the second alternative together with the theorem \nlbmath{\inpit{\ident{N}}}
is to be preferred in theorem proving for its usefulness and elegance. 
See \cite{wirthcardinal} for more on this.}
\newcommand\Diplomarbeit{Diplomarbeit (\Mastersthesis)}
\newcommand\Dissertation{Dissertation (\PhDthesis)}
\newcommand\EcoleNormaleSuperieure{\'Ecole Normale Sup\'erieure}
\newcommand\ed   {ed.}
\newcommand\Ed   {Ed.}
\newcommand\eds  {eds.}
\newcommand\edn  {edn.}
\newcommand\Edn  {Edn.}
\newcommand\eg   {e.g.}
\newcommand\Eg   {E.g.}
\newcommand\Esp  {Esp.}
\newcommand\esp  {esp.}
%\newcommand\etal{\&al.}%name already use by jsc style.
\newcommand\etalabbrev{{\namefont\&al.}}
\newcommand\etc  {\&c.}
\newcommand\etclong{etc.}
\newcommand\exfalsoquodlibet{ex falso quodlibet}
\newcommand\extd {extd.}
\newcommand\Extd {Extd.}
\newcommand\reductioadabsurdum{{\it argumentum ad absurdum}}
% these are synonyms, but as it is a deduction and not a reduction,
% one should always use "argumentum"
\newcommand\areductioadabsurdum{an \reductioadabsurdum}
\newcommand\sententialtautology{sentential tautology}
\newcommand\SententialTautology{Sentential Tautology}
\newcommand\sententialtautologies{sentential tautologies}
\newcommand\substitutionalsententialtautology
{substitutional sentential tautology}
\newcommand\substitutionalsententialtautologies
{substitutional sentential tautologies}
\newcommand\signatureenlarge     {enrich}
\newcommand\signatureenlarges    {enriches}
\newcommand\signatureenlarging   {enriching}
\newcommand\signatureenlarged    {enriched}
\newcommand\signatureenlargedby  {enriched with}
\newcommand\signatureenlargement {enrichment}
\newcommand\Signatureenlargement {Enrichment}
\newcommand\sr   {Sr.}
\newcommand\asignatureenlargement{an enrichment}
\newcommand\firstorder{first-order}
\newcommand\Firstorder{First-order}
\newcommand\FirstOrder{First-Order}
\newcommand\fol  {following}
\newcommand\ibid {ibid.} % ibidem, at the same place.
\newcommand\ie   {i.e.}
\newcommand\Ie   {I.e.}
\newcommand\incl {incl.}
\newcommand\uiff {\ iff\ }
\newcommand\udiff{\ if\ }
\newcommand\HumanOrientedInteractiveATP
{Human-Oriented Interactive Automated Theorem Proving}
\newcommand\ITP  {Inductive Theorem Proving}
\newcommand\Jun  {June}
\newcommand\Jul  {July}
% \newcommand\Log  {Log.}
\newcommand\LK   {{LK}}
\newcommand\LJ   {{LJ}}
\newcommand\Ltd  {Ltd.}
\newcommand\May  {May}
\newcommand\Mar  {March}
\newcommand\Mastersthesis{Master's thesis}
\newcommand\mastersthesis{master's thesis}
\newcommand\MSc  {M.Sc.}
\newcommand\MrUS {Mr.}
\newcommand\MrpluralUS{Messrs.}
\newcommand\mutatismutandis{mutatis mutandis}
\newcommand\Mutatismutandis{Mutatis mutandis}
\newcommand\ND   {Natural Deduction}
% There is an alternative by \usepackage{proof} and 
% \infer*{#2}{[#1]} that does four nice dots in between.
\newcommand\nonpermutable{non-permu\-ta\-ble}
\newcommand\nonpermutability{non-permu\-ta\-bi\-lity}
\newcommand\NonPermutability{Non-Permu\-ta\-bi\-lity}
\newcommand\nonpermutabilities{non-permu\-ta\-bi\-li\-ties}
\newcommand\NonPermutabilities{Non-Permu\-ta\-bi\-li\-ties}
\newcommand\negbyfail{negation as failure}
\def\note{Note}
\newcommand\notes{Notes}
%note that \note determines \litnoteref and \noteref.
\newcommand\Oct  {Oct.}
\newcommand\p    {p.}
\newcommand\pp   {pp.}
\newcommand\PP[2]{\pp\,\ignorespaces#1--\ignorespaces#2}
% Like \pp but gets first and last page as arguments
\newcommand\PPcount[1]{#1\,\pp}
\newcommand\PhD  {PhD}%{Ph.D.}
\newcommand\PhDthesis{\PhD\ thesis}
\newcommand\PhDThesis{\PhD\ Thesis}
\newcommand\Proc {Proc.}
\newcommand\proofread{proo\fri ead}
\newcommand\pnc  {posi\-tive/ne\-ga\-tive-condi\-tional}
\newcommand\Pnc  {Posi\-tive/ne\-ga\-tive-condi\-tional}
\newcommand\PNC  {Posi\-tive/Ne\-ga\-tive-Condi\-tional}
\newcommand\prep {prep.}
\newcommand\Publ {Publ.}
\newcommand\Quart{Quart.}
\newcommand\resp {resp.}
\newcommand\rev  {rev.}
\newcommand\Rev  {Rev.}
\newcommand\secondorder{second-order}
\newcommand\Secondorder{Second-Order}
\newcommand\sect {\myparagraphsymbol} 
%note that \sect determines \litsectref and \sectref.
\newcommand\sects{\myparagraphsymbol\myparagraphsymbol}
\newcommand\thissect{this \nolinebreak\sect}
\newcommand\Sci  {Sci.}
\newcommand\sic  {sic}
\newcommand\unary{singulary} % Following Quine's Mathematical Logic, p. 13:
% singulary, binary, ternary, quaternary, quinary
\newcommand\singulary{singulary}
\newcommand\Singulary{Singulary}
\newcommand\nullary  {nullary}
\newcommand\Soc  {Soc.}
\newcommand\substitutionlemma{{\sc Substitution \opt{Value} Lemma}}
\newcommand\explicitnesslemma{{\sc Explicitness Lemma}}
\newcommand\valuationlemma   {{\sc Valuation Lemma}}
\newcommand\foralllemma      {{\sc\math\forall-Lemma}}
\newcommand\existslemma      {{\sc\math\exists-Lemma}}
\newcommand\implieslemma     {{\sc\tightimplies-Lemma}}
%\newcommand\undlemma         {{\sc\tightund-Lemma}}
\newcommand\negationlemma    {{\sc\tight\neg-Lemma}}
\newcommand\vel  {vel}
\newcommand\vs   {vs.}
\newcommand\wellformed{well-formed}
\newcommand\wellformedness{well-formed\-ness}
\newcommand\wellfounded{well-founded}
\newcommand\WellFounded{Well-Founded}
\newcommand\nonwellfounded{non-well-founded}
\newcommand\wellfoundedness{well-founded\-ness}
\newcommand\Wellfoundedness{Well-founded\-ness}
\newcommand\WellFoundedness{Well-Founded\-ness}
\newcommand\wellordered{well-ordered}
\newcommand\wellorderedness{well-ordered\-ness}
\newcommand\wellordering{well-ordering}
\newcommand\Wellordering{Well-ordering}
\newcommand\WellOrdering{Well-Ordering}
\newcommand\WellOrderingTheorem{Well-Ordering Theorem}
\newcommand\wellorderingtheorem{\WellOrderingTheorem}
\newcommand\wrog {w.l.o.g.} % My favorite misspelling. Moreover \wlog is
\newcommand\Wrog {W.l.o.g.} % already a latex command
\newcommand\wrt  {w.r.t.}
\newcommand\Wrt  {W.r.t.}
\newcommand\WWWhomepage{\WWW-home-page}
\newcommand\WYSIWYG{WYSIWYG}
\newcommand\zornslemmaindexsee{\index{Zorn's Lemma|see{choice, Zorn's Lemma}}}
\newcommand\zornslemma{\index{choice!Zorn's Lemma}\zorn's Lemma}
%Abbreviations: German
\newcommand\Abs{Abs.}
\newcommand\bzw{bzw\hskip-.08em.}
\newcommand\Dasheisst{D.\nolinebreak\,h.}
\newcommand\dasheisst{d.\nolinebreak\,h.}%\dh already defined
\newcommand\dasist{d.\nolinebreak\,i.}
\newcommand\Dez{Dez.}
\newcommand\exkl{exkl.}
\newcommand\ggf{ggf.}
\newcommand\geb{geb.}
\newcommand\Ges{Ges.}
\newcommand\Ing{Ing.}
\newcommand\inkl{inkl.}
\newcommand\Jh{Jh.}
\newcommand\lt{lt.}
\newcommand\Mae{M\ae rz}
\newcommand\Mai{Mai}
\newcommand\Juni{Juni}
\newcommand\MwSt{M\hskip-0.06emwSt.}
\newcommand\Nr{Nr.}
\newcommand\oa{o.\penalty100\,a.}
\newcommand\oViA{o.V.\penalty100\,i.\penalty100\,A.}
\newcommand\Okt{Okt.}
\newcommand\reell{re\unprotectedewithtrema ll}
\newcommand\so{s.o.}
\newcommand\St{St.}
\newcommand\Staatl{Staatl.}
\newcommand\Str{Str.}
\newcommand\Suppl{Suppl.}
\newcommand\ua{u.\penalty100\,a.} % und andere
\newcommand\usw{usw.}
\newcommand\vgl{vgl.}
\newcommand\Vgl{Vgl.}
\newcommand\vglnlb{\vgl\nolinebreak}
\newcommand\zB{z.\penalty100\,B.}
\newcommand\ZB{Z.\penalty100\,B.}
\newcommand\zT{z.\penalty100\,T.}
\newcommand\ZT{Z.\penalty100\,T.}
\newcommand\zHd{z.\penalty100\,H.}

\newcommand\pncgerman{posi\-tiv/ne\-ga\-tiv be\-dingt}
\newcommand\constructorbasedgerman{kon\-struk\-tor\-ba\-siert}
\newcommand\Inferenzsystem{In\-ferenz\-sy\esi tem}
\newcommand\Rahmeninferenzsystem{Rah\-men\-in\-ferenz\-sy\esi tem}
\newcommand\Inferenzregel{In\-ferenz\-re\-gel}
\newcommand\Termersetzungssystem{Term\-er\-setzung\esi sy\esi tem}
\newcommand\gegenueber{ge\-gen\-\ue ber}
\newcommand\Beweissteuerungskonzept{Be\-wei\esi steue\-rung\esi kon\-zept}

% references

\newcommand\Axioms{Axioms}
\newcommand\thewordand{and}
\newcommand\litspageref[1]{Page\,#1}
\newcommand\litspagerefs[2]{Pages #1 \nolinebreak \thewordand\ \nolinebreak #2}
\newcommand\litspagerefss[3]{Pages #1, #2 \thewordand\ \nolinebreak #3}
\newcommand\litspagefromtoref[2]{Pages \nolinebreak #1--#2}
\newcommand\litconjref[1]{Conjecture\,#1}
\newcommand\litfootref[1]{Footnote\,#1}
\newcommand\litrequref[1]{Requirement\,#1}
\newcommand\litnoteref[1]{\note\,#1}
\newcommand\litremaref[1]{Remark\,#1}
\newcommand\itemname{item}
\newcommand\Itemname{Item}
\newcommand\litItemref[1]{\Itemname\,#1}
\newcommand\lititemref[1]{\itemname\,#1}
\newcommand\litfiguref[1]{Figure\,#1}
\newcommand\litslidref[1]{Slide\,#1}
\newcommand\litprobref[1]{Problem\,#1}
\newcommand\littheoref[1]{\theo\,#1}
\newcommand\litsectref[1]{\sect\,#1} %previously called \sectimm
\newcommand\nlblitsectref[1]{\nolinebreak\litsectref{#1}}
\newcommand\litchapref[1]{Chapter\,#1} %{\sect\,#1}
\newcommand\litchapwithsectref[2]{Chapter\,#1, \sect\,#2}%{\sect\,#1.#2} 
\newcommand\litnotefromtoref[2]{\notes\,#1--#2}
\newcommand\litchapfromtoref[2]{Chapters\,#1--#2}
\newcommand\litsectfromtoref[2]{\sects\,#1--#2}%previously called \sectfromtoimm
\newcommand\lititemfromtoref[2]{\itemname s #1 \nolinebreak to \nolinebreak #2}
\newcommand\litdefiref[1]{\defi\,#1}
\newcommand\Examplename{Ex\-am\-ple}
\newcommand\litexamref[1]{\Examplename\,#1}
\newcommand\litcoexref[1]{Counter\-ex\-am\-ple\,#1}
\newcommand\litlemmref[1]{Lem\-ma\,#1}
\newcommand\litaxioref[1]{Axiom\,#1}
\newcommand\litcororef[1]{Corol\-lary\,#1}
\newcommand\litpropref[1]{Pro\-po\-si\-tion\,#1}
\newcommand\litproprefs[2]
{Pro\-po\-si\-tions \nolinebreak #1 \thewordand\ \nolinebreak #2}
\newcommand\litrequrefs
[2]{Require\-ments  \nolinebreak #1 \thewordand\ \nolinebreak #2}
\newcommand\lititemrefs
[2]{items           \nolinebreak #1 \thewordand\ \nolinebreak #2}
\newcommand\litexamrefs[2]{Examples~#1~\thewordand~#2}
\newcommand\litcoexrefs[2]
{Counterexamples \nolinebreak #1 \thewordand\ \nolinebreak #2}
\newcommand\litlemmrefs[2]
{Lem\-mas        \nolinebreak #1 \thewordand\ \nolinebreak #2}
\newcommand\litaxiorefs[2]
{\Axioms\        \nolinebreak #1 \thewordand\ \nolinebreak #2}
\newcommand\litcororefs[2]
{Co\-rol\-laries \nolinebreak #1 \thewordand\ \nolinebreak #2}
\newcommand\littheorefs[2]
{Theorems        \nolinebreak #1 \thewordand\ \nolinebreak #2}
\newcommand\litnoterefs[2]
{\notes\         \nolinebreak #1 \thewordand\ \nolinebreak #2}
\newcommand\litsectrefs[2]
{\sects\         \nolinebreak #1 \thewordand\ \nolinebreak #2}
\newcommand\litfigurefs[2]
{Figures         \nolinebreak #1 \thewordand\ \nolinebreak #2}
\newcommand\litchaprefs[2]
{Chapters        \nolinebreak #1 \thewordand\ \nolinebreak #2}
\newcommand\litdefirefs[2]
{Definitions     \nolinebreak #1 \thewordand\ \nolinebreak #2}
\newcommand\lititemrefss
[3]{Items \nolinebreak #1, #2, \thewordand\ \nolinebreak #3}
\newcommand\litdefirefss
[3]{Definitions \nolinebreak #1, #2, \thewordand\ \nolinebreak #3}
\newcommand\litexamrefss
[3]{Examples \nolinebreak #1, #2, \thewordand\ \nolinebreak #3}
\newcommand\litexamrefsss
[4]{Examples \nolinebreak #1, #2, #3, \thewordand\ \nolinebreak #4}
\newcommand\litexamrefssss
[5]{Examples \nolinebreak #1, #2, #3, #4 \thewordand\ \nolinebreak #5}
\newcommand\litlemmrefss
[3]{Lemmas \nolinebreak #1, #2, \thewordand\ \nolinebreak #3}
\newcommand\litaxiorefss
[3]{\Axioms\ \nolinebreak #1, #2, \thewordand\ \nolinebreak #3}
\newcommand\litcororefss
[3]{Co\-rol\-laries \nolinebreak #1, #2, \thewordand\ \nolinebreak #3}
\newcommand\litnoterefss
[3]{\notes\ \nolinebreak #1, #2, \thewordand\ \nolinebreak #3}
\newcommand\litnoterefsss
[4]{\notes\ \nolinebreak #1, #2, #3, \thewordand\ \nolinebreak #4}
\newcommand\litsectrefss
[3]{\sects\ \nolinebreak #1, #2, \thewordand\ \nolinebreak #3}
\newcommand\litsectrefsss
[4]{\sects\ \nolinebreak #1, #2, #3, \thewordand\ \nolinebreak #4}
\newcommand\litsectrefssss
[5]{\sects\ \nolinebreak #1, #2, #3, #4, \thewordand\ \nolinebreak #5}
\newcommand\litfigurefss
[3]{Figures \nolinebreak #1, #2, \thewordand\ \nolinebreak #3}
\newcommand\spageref[1]{\litspageref{\pageref{#1}}}
\newcommand\spagerefs[2]{\litspagerefs{\pageref{#1}}{\pageref{#2}}}
\newcommand\specref[1]{Spec.\,\ref{#1}}
\newcommand\requref[1]{\litrequref{\ref{#1}}}
\newcommand\conjref[1]{\litconjref{\ref{#1}}}
\newcommand\remaref[1]{\litremaref{\ref{#1}}}
\newcommand\slidref[1]{\litslidref{\ref{#1}}}
\newcommand\probref[1]{\litprobref{\ref{#1}}}
\newcommand\cororef[1]{\litcororef{\ref{#1}}}
\newcommand\lemmref[1]{\litlemmref{\ref{#1}}}
\newcommand\axioref[1]{\litaxioref{\ref{#1}}}
\newcommand\examref[1]{\litexamref{\ref{#1}}}
\newcommand\coexref[1]{\litcoexref{\ref{#1}}}
\newcommand\defiref[1]{\litdefiref{\ref{#1}}}
\newcommand\theoref[1]{\littheoref{\ref{#1}}}
\newcommand\itemref[1]{\lititemref{\ref{#1}}}
\newcommand\figuref[1]{\litfiguref{\ref{#1}}}
\newcommand\noteref[1]{\litnoteref{\ref{#1}}}
\newcommand\sectref[1]{\litsectref{\ref{#1}}}
\newcommand\nlbsectref[1]{\nolinebreak\sectref{#1}}
\newcommand\sectrefff[1]{\litsectref{\ref{#1}\,\ff\ \ignorespaces}}
\newcommand\Sectref[1]{\litsectref{\ref{#1}}}
\newcommand\itemrefs[2]{\lititemrefs{\ref{#1}}{\ref{#2}}}
\newcommand\requrefs[2]{\litrequrefs{\ref{#1}}{\ref{#2}}}
\newcommand\defirefs[2]{\litdefirefs{\ref{#1}}{\ref{#2}}}
\newcommand\lemmrefs[2]{\litlemmrefs{\ref{#1}}{\ref{#2}}}
\newcommand\axiorefs[2]{\litaxiorefs{\ref{#1}}{\ref{#2}}}
\newcommand\examrefs[2]{\litexamrefs{\ref{#1}}{\ref{#2}}}
\newcommand\coexrefs[2]{\litcoexrefs{\ref{#1}}{\ref{#2}}}
\newcommand\cororefs[2]{\litcororefs{\ref{#1}}{\ref{#2}}}
\newcommand\theorefs[2]{\littheorefs{\ref{#1}}{\ref{#2}}}
\newcommand\noterefs[2]{\litnoterefs{\ref{#1}}{\ref{#2}}}
\newcommand\sectrefs[2]{\litsectrefs{\ref{#1}}{\ref{#2}}}
\newcommand\figurefs[2]{\litfigurefs{\ref{#1}}{\ref{#2}}}
\newcommand\sectfromtoref[2]{\litsectfromtoref{\ref{#1}}{\ref{#2}}}
\newcommand\notefromtoref[2]{\litnotefromtoref{\ref{#1}}{\ref{#2}}}
\newcommand\globalrequirementref[1]{\globalrequirement\,\ref{#1}}
\newcommand\itemrefss[3]{\lititemrefss{\ref{#1}}{\ref{#2}}{\ref{#3}}}
\newcommand\defirefss[3]{\litdefirefss{\ref{#1}}{\ref{#2}}{\ref{#3}}}
\newcommand\examrefss[3]{\litexamrefss{\ref{#1}}{\ref{#2}}{\ref{#3}}}
\newcommand\examrefsss[4]
             {\litexamrefsss{\ref{#1}}{\ref{#2}}{\ref{#3}}{\ref{#4}}}
\newcommand\examrefssss[5]
  {\litexamrefssss{\ref{#1}}{\ref{#2}}{\ref{#3}}{\ref{#4}}{\ref{#5}}}
\newcommand\noterefss[3]{\litnoterefss{\ref{#1}}{\ref{#2}}{\ref{#3}}}
\newcommand\noterefsss[4]{\litnoterefsss{\ref{#1}}{\ref{#2}}{\ref{#3}}{\ref{#4}}}
\newcommand\lemmrefss[3]{\litlemmrefss{\ref{#1}}{\ref{#2}}{\ref{#3}}}
\newcommand\axiorefss[3]{\litaxiorefss{\ref{#1}}{\ref{#2}}{\ref{#3}}}
\newcommand\cororefss[3]{\litcororefss{\ref{#1}}{\ref{#2}}{\ref{#3}}}
\newcommand\sectrefss[3]{\litsectrefss{\ref{#1}}{\ref{#2}}{\ref{#3}}}
\newcommand\sectrefsss
[4]{\litsectrefsss{\ref{#1}}{\ref{#2}}{\ref{#3}}{\ref{#4}}}
\newcommand\sectrefssss
[5]{\litsectrefssss{\ref{#1}}{\ref{#2}}{\ref{#3}}{\ref{#4}}{\ref{#5}}}
\newcommand\figurefss[3]{\litfigurefss{\ref{#1}}{\ref{#2}}{\ref{#3}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%% here starts the \nth macro %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% It gets an integer or a character as argument and prints e.g. 
%%% \nth{1}    --->   1st
%%% \nth{11}   --->  11th
%%% \nth{21}   --->  21st
%%% \nth{-31}  ---> -31th
%%% \nth n     ---> nth
%%% \nth q     ---> qth
%%% \nth{nn}   ---> NONSENSE
%%% some more computation features provided
%%% uses count 0-5
%%% \mth      is like \nth but sets base  number in math mode
%%% \nonumbermth is like \mth, but does not work for numbers,
%%%              but for whole mathematical expressions
%%% \nonumbermst is like \nonumbermth, but puts ``st''
%%% \smallnth is like \nth but sets power text tiny
% \newcommand\nth[1]{#1\/\math{^{\hbox{\scriptsize th}}}}
% this was raising too much! And too stupid!
%\newcommand\nth[1]{\nthpositioner{#1}{\nthstring{#1}}}
%This was too big.
\newcommand\nthpositioner[2]
% do not put something around the #1! It may remove relevant font information.
{#1\raisebox{0.52ex}{\scriptsize\hspace{0.07em}#2}}
\newcommand\nth[1]{\nthtinypositioner{#1}{\nthstring{#1}}}
\newcommand\nthtinypositioner[2]{#1\raisebox{0.52ex}{\tiny\hspace{0.07em}#2}}
\newcommand\mth[1]{\mthpositioner{#1}{\nthstring{#1}}}
\newcommand\mthpositioner[2]
% do not put something around the #1! It may remove relevant font information.
{\math{#1}\raisebox{0.52ex}{\scriptsize\hspace{0.07em}#2}}
\newcommand\modulointocountzero[2]
{\count1=#1
\count2=#2
\count0=\count1
\divide  \count0 by \count2
\multiply\count0 by-\count2
\advance \count0 by \count1}
\newcommand\absolutevalueintocountzero[1]
{\count0=#1
\ifnum\count0<0\multiply\count0 by -1\fi}
\newcommand\nthstring[1]
{\def\myargone{#1}\ifcat a\myargone th\else\nthstringnochar{#1}\fi}
\newcommand\nthstringnochar[1]
{\absolutevalueintocountzero{#1}%
\modulointocountzero{\count0}{100} %we need the blank here!
\ifnum\count0>9\ifnum\count0<20 th\else\stupidnthstring\fi
                                  \else\stupidnthstring\fi}
\newcommand\stupidnthstring
{\modulointocountzero{\count0}{10}
\ifnum\count0=1 \hskip-0.2em st\else
\ifnum\count0=2 nd\else
\ifnum\count0=3 rd\else 
                th\fi\fi\fi}
\newcommand\nonumbermth[1]{\mthpositioner{#1}{th}}
\newcommand\nonumbermst[1]{\mthpositioner{#1}{st}}

\newcommand\writeascents
%writes and integer abc as a.bc
% 0   --> 0.00
% 123 --> 1.23
[1]{\count4=#1
\ifnum\count4<0 
-\multiply\count4 by -1\fi
\modulointocountzero{\count4}{10}
\divide\count4 by 10
\count3=\the\count0
\modulointocountzero{\count4}{10}
\divide\count4 by 10
\the\count4
.\the\count0
\the\count3
}

\newcommand\frenchnth[1]{\nthtinypositioner{#1}{\frenchnthstring{#1}}}
% this work correctly only for 1 and 2 by now!
\newcommand\frenchnthstring[1]
{\def\myargone{#1}\ifcat a\myargone th\else\frenchnthstringnochar{#1}\fi}
\newcommand\frenchnthstringnochar[1]
{\absolutevalueintocountzero{#1}%
\modulointocountzero{\count0}{100} %we need the blank here!
\ifnum\count0>9\ifnum\count0<20 th\else\frenchstupidnthstring\fi
                                  \else\frenchstupidnthstring\fi}
\newcommand\frenchstupidnthstring
{\modulointocountzero{\count0}{10}
\ifnum\count0=1 \hskip-0.2em re\else
\ifnum\count0=2 me\else
\ifnum\count0=3 rd\else 
                th\fi\fi\fi}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%% here ends the \nth macro %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Systems %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand\ACLTWO    {\index{ACL2@{\sc ACL2}}{\sc ACL2}}
\newcommand\ASCII     {{\sc Ascii}}
\newcommand\ACTIVEMATH{\mbox{\sc ActiveMath}}
\newcommand\AUTOMATH  {\mbox{\sc AutoMath}}
\newcommand\BAROQUE   {\index{Baroque@{\sc Baroque}}{\sc Baroque}}
\newcommand\C         {{\sc C}}
\newcommand\CLAM      {{\rm CL\kern-.36em\raise.39ex\hbox{\sc a}\kern-.15emM}}
\newcommand\COQ       {\index{Coq@{\sc Coq}}{\sc Coq}}
\newcommand\CORE      {{\sc CoRe}}
\newcommand\DAMIT     {DaMiT}
\newcommand\INKA      {\index{Inka@{\sc Inka}}{\sc Inka}}
\newcommand\INTWOMATH {In2Math}
\newcommand\MATHWEB   {{\sc MathWeb}}
\newcommand\OANTS     {\math\Omegaoffont{\sc Ants}}
\newcommand\OPENMATH  {{\sc OpenMath}}
\newcommand\RRL       {\index{Rrl@{\sc Rrl}}{\sc Rrl}}
\newcommand\SPIKE     {\index{Spike@{\sc Spike}}{\sc Spike}}
\newcommand\TPS       {{\sc TPS}}
\newcommand\THMindexstart{\index{Thm@{\sc Thm}|(}}
\newcommand\THMindexend{\index{Thm@{\sc Thm}|)}}
\newcommand\THM       {\index{Thm@{\sc Thm}}{\sc Thm}}
\newcommand\QTHM      {\index{Qthm@{\sc Qthm}}{\sc Qthm}}
\newcommand\NQTHM     {\index{Nqthm@{\sc Nqthm}}{\sc Nqthm}}
\newcommand\NUPRL     {\index{Nuprl@{\sc Nuprl}}{\sc Nuprl}}
\newcommand\PROLOG    {\index{Prolog@{\sc Prolog}}{\sc Prolog}}
\newcommand\PERL      {{\sc Perl}}
\newcommand\OMEGA     {\math\Omegaoffont{\sc mega}} 
\newcommand\OYSTER    {{\sc Oyster}}
\newcommand\OYSTERCLAM{\index{Oyster/CLAM@{\OYSTER/\CLAM}}\OYSTER/\CLAM}
\newcommand\LCF       {\index{LCF@{\sc LCF}}{\sc LCF}}
\newcommand\LEOII     {\index{Leo-II@{\sc Leo-II}}\mbox{\sc Leo-II}}
\newcommand\LAMBDACLAM{{\sc \math\lambda\CLAM}}
\newcommand\LATEXML   {{\sc \LaTeX ML}}
\newcommand\ISAPLANNER{\index{IsaPlanner@{\sc IsaPlanner}}{\sc Isa\-Plan\-ner}}
\newcommand\LOUI      {{\sc L}\math\Omegaoffont{\sc UI}} 
\newcommand\LISPnoindex{{\sc LISP}}
\newcommand\LISP      {\index{LISP@\LISPnoindex}\LISPnoindex}
\newcommand\COMMONLISP{\index{Common Lisp@{\sc Common Lisp}}{\sc Common Lisp}}
\newcommand\JAVA      {{\sc Java}} 
\newcommand\HASKELL   {\index{Haskell@{\sc Haskell}}{\sc Haskell}}
\newcommand\CURRY     {{\sc Curry}}
% \newcommand\EBPURELISPTP{{\sc\EB\ Pure LISP Theorem Prover}}
\newcommand\PURELISPTP{\index
          {Pure LISP Theorem Prover@{\sc Pure \LISPnoindex\ Theo\-rem Pro\-ver}}%
                                            {\sc Pure \LISP\ Theo\-rem Pro\-ver}}
\newcommand\FORTRAN   {{\sc Fortran}} 
\newcommand\QUODLIBET {\index{QuodLibet@{\sc Quod\-Libet}}{\sc Quod\-Libet}}
\newcommand\QML       {{\sc Qml}} 
\newcommand\TECTON    {{\sc Tec\-ton}} 
\newcommand\TEXMACS   {{\sc T\kern-.1667em\lower.5ex\hbox{E}\kern-.125emX\kern-.1em\lower.5ex\hbox{\textsc{m\kern-.05ema\kern-.125emc\kern-.05ems}}}}
\newcommand\XQUODLIBET{{\sc XQuod\-Libet}} 
\newcommand\EXPANDER  {\index{Expander{\sc Expander}}{\sc Expander}} 
\newcommand\XEXPANDER {{\sc eXpander}} 
\newcommand\UNICOM    {\index{Unicom@{\sc Unicom}}{\sc Unicom}}
\newcommand\KNUTHBENDIX{\knuth--\bendix}
\newcommand\PREX{\mbox{\itshape P\hspace{-2pt}.\hspace{1pt}rex\/}}
\newcommand\MBASE{{\sc MBase}}
\newcommand\ml        {\index{ml@{\sc ml}}{\sc ml}}
\newcommand\MLshort   {{\sc ML}}
\newcommand\NFshort   {{\sc NF}}
\newcommand\MLlong    {\quine'\es\ \nolinebreak\MLshort}
\newcommand\NFlong    {\quine'\es\ \nolinebreak\NFshort}
\newcommand\ISABELLE  {\index{Isabelle}{\sc Isa\-belle}}
\newcommand\HOL       {\index{HOL@{\sc HOL}}{\sc HOL}}
\newcommand\ISABELLEHOL{\index{Isabelle/HOL}{\sc Isa\-belle}/\HOL}
\newcommand\Pascal{{\sc Pascal}}
\newcommand\PVS{\index{PVS@{\sc PVS}}{\sc PVS}}
\newcommand\SATALLAX{\index{Satallax@{\sc Satallax}}{\sc Satallax}}
\newcommand\SystemB{System\,(B)}
\newcommand\SystemZwithoutSystem{(Z)}
\newcommand\SystemZ{System\,\SystemZwithoutSystem}
\newcommand\VAMPIRE{{\sc Vampire}}
\newcommand\VERIFUN{{\normalsize\math{\checkmark\!\!}}{\footnotesize\sc eriFun}}
\newcommand\VSE{{\sc VSE}}
\newcommand\XML{{\sc XML}}
\newcommand\WALDMEISTER{\index
                            {Waldmeister@{\sc Wald\-Meister}}{\sc Wald\-Meister}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Institutions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand\DFGenglish{German Research \Assoc}
\newcommand\DFKI{\mbox{DFKI}}
\newcommand\ags{AG Siekmann}
\newcommand\CMU{Carnegie Mellon \Univ}
\newcommand\MIT{\mbox{MIT}}
\newcommand\theMIT{\MIT}
%J
% "from the MIT" should probably be "from MIT".
% I think it is because `MIT' has become a proper noun
% and not just an abbreviation for `Massachusetts
% Institute of Technology.'  I've never seen `the MIT'
% written before.  By the way, `the MIT' occurs in
% multiple places on page 3 and so you should do a global
% search.
\newcommand\MPIIabbrev{MPI-INF}
\newcommand\MPII{\plancknamenonamefont\ \Inst\ f\ue r Informatik} 
\newcommand\MPIIenglish{\plancknamenonamefont\ \Inst\ for Informatics} 
\newcommand\MPIIenglishlong{\plancknamenonamefont\ Institute for Informatics} 
\newcommand\UCBerkeley{\Univ\ of \California, \Berkeley}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Geographic Places %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand\Aberdeen       {Aber\-deen}
\newcommand\Amsterdam      {Amster\-dam}
\newcommand\Augsburg       {Aug\esi burg}
\newcommand\Avignon        {Avignon}
\newcommand\California     {California}
\newcommand\Cambridge      {Cam\-bridge}
\newcommand\CambridgeMassachusetts{Cam\-bridge (MA)}
\newcommand\Chicago        {Chicago}
\newcommand\Cologne        {Cologne}
\newcommand\Berkeley       {Berkeley}
\newcommand\Berlin         {Ber\-lin}    
\newcommand\Bologna        {Bologna}
\newcommand\Boston         {Boston}
\newcommand\Breslaulocal   {Bre\esi lau}
\newcommand\Breslau        {Wroc\l aw (\ie\ \Breslaulocal, Silesia)}
\newcommand\Buffalo        {Buffalo (NY)}    
\newcommand\Budapest       {Budapest}
\newcommand\DO             {Dort\-mund}
\newcommand\Dagstuhl       {Dag\-stuhl}
\newcommand\Darmstadt      {Darm\-stadt}
\newcommand\Diez           {Diez}
\newcommand\EB             {Edin\-burgh}
\newcommand\ForrestHillEB  {Forrest Hill} %Sic!
\newcommand\FFM            {Frank\-furt am Main}
\newcommand\Freiburg       {Freiburg (Breisgau)}
\newcommand\Genf           {Gen\`eve}
\newcommand\Genua          {Genova}
\newcommand\Glasgow        {Glasgow}
\newcommand\Goettingen     {G\oe ttingen}
\newcommand\Halle          {Halle an der Saale}
\newcommand\Hamburg        {Ham\-burg}
\newcommand\Harvard        {Har\-vard}
\newcommand\Hildesheim     {Hilde\esi heim (Germany)}
\newcommand\Heidelberg     {Heidel\-berg}
\newcommand\Helsinki       {Helsingfor\es}
\newcommand\Innsbruck      {Inn\esi bruck}
\newcommand\Jena           {Jena}
\newcommand\KA             {Karl\esi ruhe}
\newcommand\KL             {Kaiser\esi lau\-tern}
\newcommand\KOlocal        {Ko\-blenz}
\newcommand\KO             {\KOlocal\ (Germany)}
\newcommand\Koeln          {K\oe ln}
\newcommand\Koenigsberg    {K\oe nig\esi berg}
\newcommand\Kopenhagen     {K\o ben\-havn}
\newcommand\Landau         {Lan\-dau}
\newcommand\LA             {Lo\es\ Angele\es\ (CA)}
\newcommand\Leipzig        {Leip\-zig}
\newcommand\London         {Lon\-don}
\newcommand\Mannheim       {Mann\-heim}
\newcommand\Manchester     {Manchester}
\newcommand\Marburg        {Mar\-burg}
\newcommand\Massachusetts  {Massachusett\es}
\newcommand\Muenchen       {M\ue n\-chen}
\newcommand\Muenster       {M\ue nster}
\newcommand\Nancy          {Nancy}
\newcommand\Napoli         {Napoli}
\newcommand\NewBrunswick   {New Brun\esi wick (NJ)}
\newcommand\NewYork        {New York}
\newcommand\Nuernberg      {N\ue rn\-berg}
\newcommand\Oslo           {Oslo}
\newcommand\Oxford         {Oxford}
\newcommand\Pontamousson   {Pont-\`a-Mousson (France)}
\newcommand\Princetonnostate{Princeton}
\newcommand\Princeton      {\Princetonnostate\ (NJ)}
\newcommand\Prag           {Prague}
\newcommand\Paris          {Pari\es}
\newcommand\SB             {Saar\-br\ue cken}
\newcommand\StanfordCA     {Stan\-ford (CA)}
\newcommand\StAndrews      {St\,Andrews}
\newcommand\StPetersburg   {\St\ Peter\-burg}
\newcommand\SaratogaSprings{Sara\-toga Springs (NY)}
\newcommand\Stuttgart      {Stutt\-gart}
\newcommand\Stanford       {Stan\-ford}
\newcommand\Torino         {Torino (\ie\ Turin, Italy)}
\newcommand\Tuebingen      {T\ue\-bin\-gen (Germany)}
\newcommand\Turkey         {Turkey}
\newcommand\Warszawa       {Warszawa}
\newcommand\WarszawaEnglish{Warsaw}
\newcommand\Washington     {Washington (DC)}
\newcommand\Wernigerode    {Werni\-gerode}
\newcommand\Wien           {Wien}
\newcommand\WI             {Wie\esi ba\-den}
\newcommand\Worms          {Worms}
\newcommand\Zuerich        {\mbox{Z\ue rich}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ADDRESSES AND NAMES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand\plzuniKL  {\mbox{67653}}
\newcommand\plzuniDO  {\mbox{44221}}
\newcommand\plzuniSB  {\mbox{66123}}
\newcommand\plzWIinnen{\mbox{65183}}
\newcommand\plzdiez   {\mbox{65582}}
\newcommand\plzdudweiler{\mbox{66125}}
\newcommand\plzwernigerode{\mbox{38855}}

\newcommand\kcl         {King's College, \London}
\newcommand\uniEB       {University of \EB}
\newcommand\uniAberdeen {University of \Aberdeen}
\newcommand\uniGlasgow  {University of \Glasgow}
\newcommand\uniStAndrews{University of \StAndrews}
\newcommand\HeriotWatt{Heriot--Watt}
\newcommand\unitexasaustin{The University of Texas at Austin}
\newcommand\uniheriotwatt{\HeriotWatt\ University}
\newcommand\uniDO{\uni\ \DO}
\newcommand\uniKO{\uni\ \KOlocal-\Landau}
\newcommand\uniKA{\uni\ \KA}
\newcommand\uniKL{\uni\ \KL}
\newcommand\uniSB{\uni\ des Saar\-lan\-de\es}
\newcommand\uniKLenglish{University of \KL}
\newcommand\uniSBenglish{Saar\-land University}
\newcommand\uniSBenglishshort{Saar\-land \Univ}

\newcommand\uniDOshort{\Univ\ \DO}
\newcommand\uniKLshort{\Univ\ \KL}
\newcommand\uniSBshort{Saar\-land \Univ}
\newcommand\uniEBshort{\Univ\ \EB}
\newcommand\uniKOshort{\Univ\ \KOlocal-\Landau}
\newcommand\uniKAshort{\Univ\ \KA}

\newcommand\addressuniKL{\FBinf, \uniKL}
\newcommand\addressuniKLshort{\FBinfshort, \uniKLshort}
\newcommand\addressuniDOshort{\FBinfshort, \uniDOshort}
\newcommand\addressuniSBshort{\FRinfshort, \uniSBshort}
\newcommand\addressuniKLcomplete
{\FBinf, \uniKL, Postfach\,3049, \plzuniKL\,\KL, Germany}
\newcommand\addressuniDOcomplete
{Informatik, \uniDO, \plzuniDO\,\DO, Germany} 
\newcommand\addressuniSBcomplete
{\FRinf, \uniSB, \plzuniSB\,\SB, Germany} 
\newcommand\addressuniKLlongwithnl
{\FBinf,\\\uniKL,\\\plzuniKL\,\KL}
\newcommand\addressuniDOlongwithnl
{Informatik,\\\uniDO,\\\plzuniDO\,\DO} 
\newcommand\addressuniKLlongwithnlwithoutcomma
{\FBinf\\\uniKL\\\plzuniKL\,\KL}
\newcommand\addressuniDOlongwithnlwithoutcomma
{Informatik\\\uniDO\\\plzuniDO\,\DO} 
\newcommand\addressuniSBlongwithnlwithoutcomma
{\FRinf\\\uniSB\\\plzuniSB\,\SB} 
\def       \emailcp      {{\tt wirth@logic.at}}
\newcommand\emailmhwithoutfontinfo{marianeh.rezaei@gmail.com}
\newcommand\emailmh      {{\tt \emailmhwithoutfontinfo}}
% {{\tt marianeh\_80@yahoo.com}}
\newcommand\Institutedept
% {\Dept\ of \CSlong}
{\FBautinfveryshort}
\newcommand\Instituteinst
% {\mbox\uniSBenglish}
{\mbox{Hochschule Harz}}
\newcommand\Instituteplac
% {\plzuniSB\,\SB}
{\plzwernigerode\,\Wernigerode}
\newcommand\Institutecoun{Germany}
\newcommand\Institutestre{Friedrichstr.\,57--59}
\newcommand\Institute
{\Institutedept, \Instituteinst, \Instituteplac, \Institutecoun}
% {\planckname\ Institute for Informatics, \plzuniSB\,\SB, Germany}
% {Brandenburger Str.\,42, \plzdiez\ \Diez, Germany}
\newcommand\Institutewithnl
{\Institutedept, \Instituteinst\\\Institutestre\\\Instituteplac\\\Institutecoun}


\newcommand\SFB        {Collaborative Research Center}
\newcommand\oursfbshort{SFB\,378}
\newcommand\oursfblong {\SFB\ \oursfbshort}
\newcommand\oursfbname {Resource-Adaptive Cognitive Processes}
\newcommand\oldsfbshort{SFB\,314}
\newcommand\oldsfblong {\SFB\ \oldsfbshort}
\newcommand\oldsfbname {AI~---~Knowledge-Based Systems}

\newcommand\Myfocusofinterest{P\myfocusofinterestrest}
\newcommand\myfocusofinterest{p\myfocusofinterestrest}
\newcommand\myfocusofinterestrest
{ractice-relevant human-oriented interactive inductive 
theorem proving in first- and higher-order logics
with strong automation support,
as exemplified by our \QUODLIBET\ and \OMEGA\ systems}
\newcommand\myareasofexpertise{%
Logic (both as creator and historian), \hskip.2em 
(Theoretical)\ Computer Science,\\Formal Methods, \hskip.2em 
\AI, \hskip.2em History of Logic and Philosophy}
\newcommand\mysubfields{%
Algebraic Specification;
Conditional Term Rewriting, Confluence Theorems; 
\hilbert's epsilon (applied!);
% (Co-) 
Inductive Theorem Proving (automated/interactive),
Free-Variable Calculi,
% Efficient Algorithms, 
% Hypertext Web Models,
Proof Planning,
\MASlong s;
History of Modern Logic and
Proof Theory (with focus on 
\hilbertbernays\ and
\herbrand)}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Citation commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% LECTURE NOTES

\newcommand\CSLILN[1]
{CSLI LN\,#1, CSLI Publications, \Stanford\ \Univ}

% SPRINGER LECTURE NOTES

% LNCS
\newcommand\LNCSvol[1]
{\mbox{LNCS}\,\ignorespaces#1}

% LNAI
\newcommand\LNAIvol[1]
{\mbox{LNAI}\,\ignorespaces#1}

% LNM
\newcommand\LNMvol[1]
{\mbox{LNM}\,\ignorespaces#1}


% Verlage---------------------------------------------------------------------
\newcommand\aaaipress{AAAI Press}
\newcommand\academicpress{Academic Press (\elsevier)}
\newcommand\ACM{ACM}
\newcommand\acmpress{\ACM\ Press}
\newcommand\addisonwesley{Addi\-son--Wes\-ley, Reading (MA)}
\newcommand\akademieverlag{Akademie Verlag GmbH, \Berlin}
\newcommand\allenandunwin{\george\ Allen \& Unwin, \London}
\newcommand\verlagchbeck{Verlag C.\,H.\,Beck% oHG
, \Muenchen}
\newcommand\basilblackwell{Basil Blackwell, \Oxford}
\newcommand\birkhaeuser{Birkh\ae user (\springerverlag)}
\newcommand\cambridgeunipress{\Cambridge\ \Univ\ Press}
\newcommand\chicagounipress{\Univ\ \Chicago\ Press}
\newcommand\univcaliforinapress
{\Univ\ of \California\ Press, \Berkeley\ and \LA}
\newcommand\clarendonpress{Clarendon Press, \Oxford\ (\oxfordunipress)}
\newcommand\collegepublications{College Publications, \London}
\newcommand\deGruyter{de\,Gruyter, \Berlin, \NewYork}
\newcommand\digitalpress{Digital Press (\elsevier)}
\newcommand\elsevier{Elsevier}
\newcommand\gauthiervillars{Gauthier-Villars, \Paris}
\newcommand\harvardunipress{\Harvard\ \Univ\ Press}
\newcommand\hermannparis{\hermann, \Paris}
\newcommand\hermannparisseries{Actu\-a\-li\-t\'es Scientifiques et Industrielles}
\newcommand\ieee{IEEE}
\newcommand\ieeepress{\ieee\ Press}
\newcommand\ieeeCSpress{\ieee\ Computer \Sci\ Press, Los Alamitos (CA)}
\newcommand\indianaunipress{Indiana \Univ\ Press}
\newcommand\infixverlag{Infix, 
Aka\-de\-mi\-sche Ver\-lags\-ge\-sell\-schaft Aka GmbH, 
Sankt Au\-gustin, \Berlin}
\newcommand\kluwer{Kluwer% Acad.\ \Publ
\ (\SPRINGER)}
\newcommand\mcgrawhill{McGraw-Hill}
\newcommand\morgankaufmannwithoutadds{Morgan Kaufmann, Los Altos (CA)}
\newcommand\morgankaufmann{Morgan Kaufmann (\elsevier), Los Altos (CA)}
\newcommand\williamkaufmann{William Kaufman}
\newcommand\mitpress{\MIT\ Press}
\newcommand\northholland{North-Holland (\elsevier)}
\newcommand\olmsverlag{Georg Olm\es\ Verlag, \Hildesheim}
\newcommand\oxfordunipress{\Oxford\ \Univ\ Press}
\newcommand\pergamonpress{Pergamon Press, \Oxford}
\newcommand\pitman{Pitman \Publ, \London%
% This has been taken over by Financial Times Press and is hard to find.
% Thus, the place should be given explicitly!
}
\newcommand\PrenticeHall{Prentice--Hall, \Inc}
\newcommand\princetonunipress{\Princetonnostate\ \Univ\ Press}
\newcommand\DReidelpublishing{D. Reidel \Publ, Dordrecht, now part of \SPRINGER}
\newcommand\sfischerverlagberlin{S. Fischer Ver\-lag, \Berlin}
\newcommand\sfischerverlagffm{S. Fischer Ver\-lag, \FFM}
\newcommand\springerverlag{Sprin\-ger}
\newcommand\SPRINGER{Springer Science+Business Media}
\newcommand\suhrkampverlagfrankfurt{Suhr\-kamp Verlag, \FFM}
\newcommand\suhrkampverlagberlin{Suhr\-kamp Verlag, \Berlin}
\newcommand\teubner{Teub\-ner}
\newcommand\teubnerverlag{B. G. \teubner\ Ver\-lag\esi ge\-sell\-schaft}
\newcommand\teubnerarchivzurmathematik[1]
{\teubner-Archiv zur Mathe\-ma\-tik, \Vol\,#1, \teubnerverlag, \Leipzig}
\newcommand\vannostrand{D. Van Nostrand}
\newcommand\vieweg{Vieweg, Braunschweig} 
\newcommand\wiley{\john\ Wiley \& Sons, \NewYork}
\newcommand\wissenschaftlichebuchgesellschaftdarmstadt
 {Wissen\-schaft\-liche Buch\-gesell\-schaft, \Darmstadt}

%Reports----------------------------------------------------------------------
\newcommand\sekireportname{SEKI-Report}
\newcommand\sekireportissn{1437--4447}
\newcommand\sekireportnoaddress[2]{\sekireportname\ \mbox{SR--#1--#2}}
\newcommand\sekireport   [2]{\sekireportnoaddress{#1}{#2}, \addressuniKLshort}
\newcommand\sekireportSB [2]{\sekireportnoaddress{#1}{#2}, \addressuniSBshort}
\newcommand\sekireportnew[2]{\sekireportnoaddress{#1}{#2}, ISSN\,1437-4447}

\newcommand\sekiworkingpapername{SEKI-Working-Paper}
\newcommand\sekiworkingpaperissn{1860--5931}
\newcommand\sekiworkingpapernoaddress[2]
{\sekiworkingpapername\ \mbox{SWP--#1--#2}}
\newcommand\sekiworkingpaper[2]{\sekiworkingpapernoaddress
{#1}{#2}, \addressuniKLshort}
\newcommand\sekiworkingpapernew[2]{\sekiworkingpapernoaddress
{#1}{#2}, ISSN\,1860-5931}

\newcommand\gruenereihe[2]{Report #2/#1, \addressuniDOshort}

\newcommand\mpireportnoaddress[2]{MPI--I--#1--2--#2}
\newcommand\mpireport[2]{\mpireportnoaddress{#1}{#2}, \MPII, \SB}

\newcommand\daireport
[1]{DAI Research Paper \Numero\,#1, \Dept\ \AI, \uniEBshort}

%Conferencen------------------------------------------------------------------
\newcommand\lncsconf[6]{\nth{#2}\,#1\,#3, #4, \PP{#5}{#6}, \springerverlag}

%AAAI
\newcommand\AAAI[4]
{\nth{#1} AAAI 19#2, \PP{#3}{#4}, \mitpress}
\newcommand\eighthAAAIninety{\AAAI{8}{90}}

%ALP1
\newcommand\fourthAlgLogPninetyfour
{\lncsconf{Algebraic and Logic Programming}{4}{1994}{\LNCSvol{850}}}

%ALP2
\newcommand\fourteenthAutLanPeightyseven
{\lncsconf{Automata, Languages and Programming}{14}{1987}{\LNCSvol{267}}}


%CAAP
\newcommand\CAAPname{\Int\ Colloquium on Trees in Algebra and Programming}
\newcommand\CAAPshort{CAAP}
\newcommand\ninthCAAPeightyfourtitle
{\Proc\ \nth 9 \CAAPname\ (\CAAPshort\,1984), Bordeaux}
%% Please use a separate bib entry!
%% \newcommand\ninthCAAPeightyfour[2]
%% {In: Bruno Courcelle (\ed): \ninthCAAPeightyfourtitle,
%%% \PP{#1}{#2}, \cambridgeunipress}
\newcommand\twentyfirstCAAPninetysix
{\lncsconf\CAAPshort{21}{1996}{\LNCSvol{1059}}}

%CADE
\newcommand\CADEname{\Int\ \Conf\ on Automated Deduction}
\newcommand\CADEshort{CADE}
\newcommand\thelocalCADE[3]{\nth{#1} \CADEname\ (\CADEshort), #3, #2}
\newcommand\thefifthCADEeighty             
{\thelocalCADE       {5}{1980}{Les Arcs (France)}}
\newcommand\fifthCADEeighty           
{\lncsconf\CADEshort {5}{1980}{\LNCSvol{  87}}}
\newcommand\theeighthCADEeightysix                
{\thelocalCADE       {8}{1986}{\Oxford}}
\newcommand\eighthCADEeightysix                  
{\lncsconf\CADEshort {8}{1986}{\LNCSvol{ 230}}}
\newcommand\theninthCADEeightyeight                
{\thelocalCADE       {9}{1988}{Argonne National Laboratory (IL)}}
\newcommand\ninthCADEeightyeight                
{\lncsconf\CADEshort {9}{1988}{\LNAIvol{ 310}}}
\newcommand\thetenthCADEninety                      
{\thelocalCADE      {10}{1990}{\KL\ (Germany)}}
\newcommand\tenthCADEninety                      
{\lncsconf\CADEshort{10}{1990}{\LNAIvol{ 449}}}
\newcommand\theeleventhCADEninetytwo             
{\thelocalCADE  {11}{1992}{\SaratogaSprings}}
\newcommand\eleventhCADEninetytwo                
{\lncsconf\CADEshort{11}{1992}{\LNAIvol{ 607}}}
\newcommand\thetwelvethCADEninetyfour            
{\thelocalCADE  {12}{1994}{Nancy}}
\newcommand\twelvethCADEninetyfour               
{\lncsconf\CADEshort{12}{1994}{\LNAIvol{ 814}}}
\newcommand\thethirteenthCADEninetysix           
{\thelocalCADE  {13}{1996}{\NewBrunswick}}
\newcommand\thirteenthCADEninetysix              
{\lncsconf\CADEshort{13}{1996}{\LNAIvol{1104}}}
\newcommand\thesixteenthCADEninetynine              
{\thelocalCADE  {16}{1999}{Trento (Italy)}}
\newcommand\sixteenthCADEninetynine              
{\lncsconf\CADEshort{16}{1999}{\LNAIvol{1632}}}
\newcommand\eightteenthCADEtwo                   
{\lncsconf\CADEshort{18}{2002}{\LNAIvol{2392}}}
\newcommand\theeightteenthCADEtwo                   
{\thelocalCADE  {18}{2002}{\Kopenhagen\ (Denmark)}}
\newcommand\nineteenthCADEthree                   
{\lncsconf\CADEshort{19}{2003}{\LNAIvol{2741}}}
\newcommand\thenineteenthCADEthree                   
{\thelocalCADE  {19}{2003}{Miami Beach (FL)}}
\newcommand\thetwentiethCADEfive
{\thelocalCADE  {20}{2005}{Tallinn}}
\newcommand\twentiethCADEfive
{\lncsconf\CADEshort{20}{2005}{\LNAIvol{3632}}}
\newcommand\thetwentythirdCADEeleven
{\thelocalCADE  {23}{2011}{\Breslau}}
\newcommand\thetwentyfourthCADEthirteen
{\thelocalCADE  {24}{2013}{Lake Placid (NY)}}

%CALCULEMUS

%CCL
\newcommand\firstCCL{\nth 1 Workshop on 
Construction of Computational Logics, Val d'Ajol (France), 1992}

%CLP
\newcommand\eighthCLPtitle
{\Proc\ \nth{8} \Int\ \Conf\ on Logic Programming}
\newcommand\twelvethCLPtitle
{\Proc\ \nth{12} \Int\ \Conf\ on Logic Programming}
%% Please use a new bib entry instead!
%% \newcommand\eighthCLP  [2]{\eighthCLPtitle,   1991, \PP{#1}{#2}, \mitpress}
%% \newcommand\twelvethCLP[2]{\twelvethCLPtitle, 1995, \PP{#1}{#2}, \mitpress}

%CSL
\newcommand\CSLname{\Conf\ of the European Association for \CS\ Logic}

%CTRS
\newcommand\CTRSname{\Int\ Workshop on Conditional Term Rewriting Systems (CTRS)}
\newcommand\CTRSshort{CTRS}
\newcommand\theCTRS[3]{\nth{#1} \CTRSname, #3, #2}
\newcommand\firstCTRSeightyseven   {\lncsconf\CTRSshort{1}{1987}{\LNCSvol{308}}}
\newcommand\thefirstCTRSeightyseven       {\theCTRS{1}{1987}{Orsay (France)}}
\newcommand\secondCTRSninety       {\lncsconf\CTRSshort{2}{1990}{\LNCSvol{516}}}
\newcommand\thesecondCTRSninety           {\theCTRS{2}{1990}{Montreal}}
\newcommand\thirdCTRSninetytwo     {\lncsconf\CTRSshort{3}{1992}{\LNCSvol{656}}}
\newcommand\thethirdCTRSninetytwo         {\theCTRS{3}{1992}{\Pontamousson}}
\newcommand\fourthCTRSninetyfour   {\lncsconf\CTRSshort{4}{1994}{\LNCSvol{968}}}
\newcommand\thefourthCTRSninetyfour       {\theCTRS{4}{1994}{Jerusalem}}

%ECAI
\newcommand\ECAIname{European \Conf\ on \AI}
\newcommand\ECAI[5]
{{\em\nth{#1} \ECAIname\ (ECAI\,#2)}, \PP{#4}{#5}, #3}
\newcommand\eighthECAIeightyeight
{{\namefont Y. Kodratoff} (\ed). \ECAI{8}{1988}{\pitman}}
% This is correct!
\newcommand\ninthECAIninety{\ECAI{9}{1990}{\pitman}}
\newcommand\eleventhECAIninetyfour
{{\namefont A. G. Cohn} (\ed). \ECAI{11}{1994}{\wiley}}

%FOCS
\newcommand\FOCSname{Annual Symposium on Foundations of Computer \Sci}

%FTP
\newcommand\FTPname{\Int\ Workshop on First-Order Theorem Proving}
\newcommand\FTPshort{FTP}

%GWAI
\newcommand\GWAIname{German Workshop on \AI\ (GWAI)}

%ICALP
\newcommand\ICALPname
               {\Int\ Colloquium on Automata, Languages and Programming (ICALP)}
\newcommand\thirteenthICALPeightysix{\lncsconf{ICALP}{13}{1986}{\LNCSvol{226}}}

%IJCAI
\newcommand\IJCAIname{\Int\ Joint \Conf\ on \AI}
\newcommand\IJCAI    {\mbox{IJCAI}}
\newcommand\eleventhIJCAIeightnine
[2]{In: {\namefont N. S. Sridharan} (\ed). 
       {\em \Proc\ \nth{11} \IJCAIname\ (\IJCAI)}, \PP{#1}{#2},
       \morgankaufmann}
\newcommand\thirteenthIJCAIninetythree
[2]{In: {\namefont Ruzena Bajcsy} (\ed). 
       {\em \Proc\ \nth{13} \IJCAIname\ (\IJCAI)}, \PP{#1}{#2},
       \morgankaufmann}
\newcommand\seventeenthIJCAIone
[2]{In: \nebelname\ (\ed). 
       {\em \Proc\ \nth{17} \IJCAIname\ (\IJCAI)}, \PP{#1}{#2},
       \morgankaufmann}

%IJCAR
\newcommand\IJCARname{\Int\ Joint \Conf\ on Automated Reasoning (IJCAR)}
\newcommand\thelocalIJCAR[3]{\nth{#1}\,\IJCARname, #3, #2}
\newcommand\firstIJCARone{\lncsconf{IJCAR}{1}{2001}{\LNAIvol{2083}}}
\newcommand \thefirstIJCARone   {\thelocalIJCAR{1}{2001}{Siena (Italy)}}
\newcommand\thefourthIJCAReight {\thelocalIJCAR{4}{2008}{Sydney (Australia)}}
\newcommand \thesixthIJCARtwelve{\thelocalIJCAR{6}{2012}{\Manchester}}

%KR

\newcommand\KRname
{\Int\ \Conf\ on Principles of Knowledge Representation and Reasoning}
\newcommand\thethirdKRninetytwo
{\nth 3\,KR\,1992 --- \KRname, {\mbox{\Oct\,26--29,}} 1992, Cambridge (MA)}
\newcommand\thirdKRninetytwo{\Proc\ \thethirdKRninetytwo}
\newcommand\thefifthKRninetysix
{\nth 5\,KR\,1996 --- \KRname, {\mbox{\Nov\,5--8,}} 1996, Cambridge (MA)}
\newcommand\fifthKRninetysix{\Proc\ \thefifthKRninetysix}
\newcommand\thefourteenthKRfourteen{\nth{14}\,KR\,2014 --- \KRname, \mbox{Jul\,20--24,} as part of the Vienna Summer of Logic, Vienna, July\,9--24, 2014}
\newcommand\fourteenthKRfourteen{\Proc\ \thefourteenthKRfourteen}

%LFCS
\newcommand\LFCSname{\Int\ Symposium on Logical Foundations of \CS}
\newcommand\LFCSshort{LFCS}
\newcommand\thirdLFCSninetyfour
{\lncsconf\LFCSshort{3}{1994}{\LNCSvol{813}}}

%LICS
\newcommand\LICSname{Annual \ieee\ Symposium on Logic In \CS\ (LICS)}
\newcommand\LICS[3]
{#1 \LICSname, \PP{#2}{#3}, \ieeepress}
\newcommand\firstLICSeightysix  {\LICS{\nth 1}}
\newcommand\thirdLICSeightyeight{\LICS{\nth 3}}
\newcommand\licsarchive{\url{http://lii.rwth-aachen.de/lics/archive/}}

%LPAR
\newcommand\LPAR{LPAR}
\newcommand\LPARname{\Int\ \Conf\ on Logic for Programming, \AI, and Reasoning}
\newcommand\thirdLPARninetytwo  {\lncsconf{LPAR} {3}{1992}{\LNAIvol {624}}}
\newcommand\fifthLPARninetyfour {\lncsconf{LPAR} {5}{1994}{\LNAIvol {822}}}
\newcommand\eleventhLPARzerofour{\lncsconf{LPAR}{11}{2004}{\LNAIvol{3452}}}
\newcommand\twelfthLPARzerofive {\lncsconf{LPAR}{12}{2005}{\LNAIvol{3835}}}

%MKM
\newcommand\MKMshort{MKM}
\newcommand\MKMname{\Int\ \Conf\ on Mathematical Knowledge Management}
\newcommand\theforthMKMfive{\nth 4 \MKMname\ (\MKMshort), Bremen, 2005}
\newcommand\fourthMKMfive{\lncsconf{MKM}{4}{2005}{\LNAIvol{3863}}}

%POPL
\newcommand\POPLname
{Annual \ACM\ SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL)}

%RTA
\newcommand\RTAname
{\Int\ \Conf\ on Rewriting Techniques and Applications (RTA)}
\newcommand\theRTA[3]
{\nth{#1} \RTAname, #3, #2}
\newcommand\thethirdRTAeightynine           {\theRTA{ 3}{1989}{Chapel Hill (NC)}}
\newcommand\thirdRTAeightynine       {\lncsconf{RTA}{ 3}{1989}{\LNCSvol{ 355}}}
\newcommand\fourthRTAninetyone       {\lncsconf{RTA}{ 4}{1991}{\LNCSvol{ 488}}}
\newcommand\thesixthRTAninetyfive           {\theRTA{ 6}{1995}{\KL\ (Germany)}}
\newcommand\sixthRTAninetyfive       {\lncsconf{RTA}{ 6}{1995}{\LNCSvol{ 914}}}
\newcommand\theseventhRTAninetysix          {\theRTA{ 7}{1996}{\NewBrunswick}}
\newcommand\seventhRTAninetysix      {\lncsconf{RTA}{ 7}{1996}{\LNCSvol{1103}}}
\newcommand\theeighthRTAninetyseven         {\theRTA{ 8}{1997}{Sitges (Spain)}}
\newcommand\eighthRTAninetyseven     {\lncsconf{RTA}{ 8}{1997}{\LNCSvol{1232}}}
\newcommand\tenthRTAninetynine       {\lncsconf{RTA}{10}{1999}{\LNCSvol{1631}}}

%STACS
\newcommand\STACSname{\Int\ Symposium on Theoretical Aspects of \CS}
\newcommand\STACSshort{STACS}
\newcommand\eleventhSTACSninetyfour{\lncsconf{STACS}{11}{1994}{\LNCSvol{775}}}

%TABLEAUX
\newcommand\TABLEAUname
{\Int\ \Conf\ on Tableaux and Related Methods}
\newcommand\TABLEAUshort{TAB\-LEAUX}
\newcommand\theTABLEAU[3]
{\nth{#1} \TABLEAUname, #3, #2}
\newcommand\thefourthTABLEAUninetyfive{\theTABLEAU{5}{1995}{\St\ Goar (Germany)} (actually still ``Workshop'' instead of ``\Conf'')}
\newcommand\fourthTABLEAUninetyfive
{\lncsconf\TABLEAUshort{4} {1995}{\LNAIvol{ 918}}}
\newcommand\thesixthTABLEAUninetyseven{\theTABLEAU{6}{1997}{\Pontamousson}}
\newcommand\sixthTABLEAUninetyseven
{\lncsconf\TABLEAUshort{6} {1997}{\LNAIvol{1227}}}
\newcommand\eighthTABLEAUninetynine
{\lncsconf\TABLEAUshort{8} {1999}{\LNAIvol{1617}}}
\newcommand\theeighthTABLEAUninetynine    
{\theTABLEAU{8} {1999}{\SaratogaSprings}}
\newcommand\ninthTABLEAUzero       
{\lncsconf\TABLEAUshort{9} {2000}{\LNAIvol{1847}}}
\newcommand\theeleventhTABLEAUtwo  
{\theTABLEAU{11}{2002}{\Kopenhagen}}
\newcommand\eleventhTABLEAUtwo     
{\lncsconf\TABLEAUshort{11}{2002}{\LNAIvol{2381}}}
\newcommand\thefourteenthTABLEAUfive{\theTABLEAU{14}{2005}{\KO}}
\newcommand\fourteenthTABLEAUfive
{\lncsconf\TABLEAUshort{14}{2005}{\LNAIvol{3702}}}


%TAPSOFT
\newcommand\TAPSOFTninetythree[2]
{TAPSOFT 1993, \LNCSvol{668}, \PP{#1}{#2}, \springerverlag}

%TPHOLs
\newcommand\TPHOLshort{TPHOLs}
\newcommand\TPHOLname{\Int\ \Conf\ on Theorem Proving in Higher-Order Logics}
\newcommand\theninthTPHOLninetysix{\nth 9 \TPHOLname\ (\TPHOLshort), Turku (Finland), 1996}
\newcommand\TPHOLninetysix[2]
{\theninthTPHOLninetysix, \LNCSvol{1125}, \PP{#1}{#2}, \springerverlag}


%UNIF
\newcommand\UNIFname{\Int\ Workshop on Unificiation}
\newcommand\UNIFshort{UNIF}

%Newspapers-------------------------------------------------------------------

\newcommand\newspaperreference[5]
{\def\nameofjournalpress{#2}#1, #4 #5, #3\if?\nameofjournalpress
\else, #2\fi}

\newcommand\nytimes{\newspaperreference{The \NewYork\ Times}?}

%Journals---------------------------------------------------------------------

\newcommand\dateinjournal[1]{}

\newcommand\journalreference[6]
{\def\nameofjournalpress{#2}#1\nolinebreak\hskip.2em%
\dateinjournal{(#3) }{\mbox{\bf #4}}, \PP{#5}{#6}\if?\nameofjournalpress
\else, #2\fi}

\newcommand\journalreferenceprintyear[6]
{\def\nameofjournalpress{#2}#1 
% {(#3) }{\bf #4}, \PP{#5}{#6}%
#4:#5--#6, #3%
\if?\nameofjournalpress
\else, #2\fi}

\newcommand\journalreferenceprintyearaspartofnumber[6]
{\def\nameofjournalpress{#2}#1 
{#4/#3}, \PP{#5}{#6}\if?\nameofjournalpress
\else, #2\fi}

\newcommand\AARname{Association for Automated Reasoning}
\newcommand\AARshort{AAR}

\newcommand\AbhandlungenmathHamburgname
{Abhandlungen au\es\ dem mathematischen Seminar der \Univ\ Hamburg}
\newcommand\AbhandlungenmathHamburg
{\journalreference
{\AbhandlungenmathHamburgname}?}

\newcommand\actacybernetica
{\journalreference{Acta Cybernetica}{Szeged}}

\newcommand\actamathematicaprintyear
{\journalreference{Acta Mathematica}?}

\newcommand\americanmathematicalmonthlyname{American Mathematical Monthly}
\newcommand\americanmathematicalmonthly
{\journalreference{\americanmathematicalmonthlyname}?}

\newcommand\americanjmath
{\journalreference{American J. of \Math}?}

\newcommand\americanscientistname
{American Scientist}

\newcommand\americanscientistprintyear
{\journalreferenceprintyear{\americanscientistname}?}

\newcommand\annalesecolesuperieur
{\journalreference{Annales Scientifiques d l'\EcoleNormaleSuperieure}?}

\newcommand\annalesuniversiteparis
{\journalreference{Annales de l'Universit\'e de \Paris}?}

\newcommand\annalsofmathematicsname{Annals of Mathematics}
\newcommand\annalsofmathematics{\journalreference{\annalsofmathematicsname}?}

\newcommand\AMAIname{Annals of Mathematics and Artificial Intelligence}

\newcommand\archivehistoryexactsciences
{\journalreference{Archive for History of Exact Sciences}\springerverlag}

\newcommand\artificialintelligencename{\AI}
\newcommand\artificialintelligence
{\journalreference{\artificialintelligencename}?}
\newcommand\artificialintelligenceprintyear
{\journalreferenceprintyear{\artificialintelligencename}?}

\newcommand\artificialintelligencetools
{\Int\ J. \AI\ Tools}
\newcommand\artificialintelligencetoolsprintyear
{\journalreferenceprintyear{\artificialintelligencetools}?}

\newcommand\artificialintelligencecommunicationsname{AI \Comm}

\newcommand\AttiAccadTorinoname{Atti della Reale Accademia delle Scienze di \Torino\ ---  Classe di Scienze Morali, Storiche e Filologiche e Classe di Scienze Fisiche, Matematiche e Naturali}
\newcommand\AttiAccadTorino
{\journalreference{\AttiAccadTorinoname}?}

\newcommand\AttiAccadTorinoFisicheMatematicheNaturali
{\journalreference{Atti della Reale Accademia delle Scienze di \Torino\ ---
Classe di Scienze Fisiche, Matematiche e Naturali}?}

\newcommand\EATCSname{European Assoc.\ for Theoretical \CS}
\newcommand\EATCSshort{EATCS}
\newcommand\bulleatcs
{\journalreference{\Bull\ \EATCSshort}?}

\newcommand\AMSname{American \Math\ \Soc}
\newcommand\AMSshort{AMS}
\newcommand\bullamsname
{\Bull\ \AMSname}
\newcommand\bullams
{\journalreference{\bullamsname}?}

\newcommand\noticesamsname{Notices of the \AMSname}
\newcommand\transamsname{Transactions of the \AMSname}

\newcommand\cahierssemhistmath
{\journalreference{Cahiers du s\'eminaire d'histoire des math\'ematiques}?}

\newcommand\comptesrendusname
{Comptes rendus hebdomadaires des s\'eances de l'Acad\'emie des Sciences 
(\Paris)}

\newcommand\comptesrendus
{\journalreference{\comptesrendusname}?}

\newcommand\computationallinguisticsname{Computational Linguistic\es}
\newcommand\computationallinguistics
{\journalreference{\computationallinguisticsname}?}

\newcommand\commacmname{\Comm\ ACM}
\newcommand\commacm
{\journalreference{\commacmname}\acmpress}

\newcommand\dmvjahresberichtname
{Jahre\esi bericht der Deutschen Mathe\-matiker-Ver\-eini\-gung}

\newcommand\dmvmitteilungenname{DMV-Mitteilungen}
\newcommand\dmvmitteilungen
{\journalreferenceprintyearaspartofnumber{\dmvmitteilungenname}?}

\newcommand\ENTCSname{Electronic Notes in Theoretical \CS}
\newcommand\ENTCS
{\journalreference\ENTCSname\elsevier}

\newcommand\erkenntisannalen{Erkenntnis (Annalen der Philosophie (und Philosophischen Kritik))}

\newcommand\forschungenname
{Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften}

\newcommand\forschungen
{\journalreference
{\forschungenname}
\Leipzig}

\newcommand\fundamentainformaticaename
{Fundamenta Informaticae}

\newcommand\fundamentainformaticae
{\journalreference{\fundamentainformaticaename}?}

\newcommand\ieicetrans
{\journalreference{IEICE Transactions}?}

\newcommand\informationandcomputationprintyear
{\journalreferenceprintyear{Information and Computation}\academicpress}
\newcommand\informationandcomputation
{\journalreference{Information and Computation}\academicpress}

\newcommand\informationandcontrol
{\journalreference{Information and Control}?}

\newcommand\historiamathematica
{\journalreference{Historia Mathematica}?}

\newcommand\historyandphilosophyoflogicname
{History and Philosophy of Logic}
\newcommand\historyandphilosophyoflogic
{\journalreference
{\historyandphilosophyoflogicname}{Taylor \& Francis, \London}}

\newcommand\aaeccname
{J. Applicable Algebra in Engineering, Communication and Computing (AAECC)}
\newcommand\aaecc
{\journalreference\aaeccname\springerverlag}
\newcommand\aaeccprintyear
{\journalreferenceprintyear\aaeccname\springerverlag}

\newcommand\ieeetranssename{\ieee\ Transactions on Software Engineering}
\newcommand\ieeetransse    {\journalreference{\ieeetranssename}\ieeepress}

\newcommand\jacmname{J. of the \ACM}
\newcommand\jacm
{\journalreference\jacmname\acmpress}

\newcommand\jalname{J. Applied Logic}
\newcommand\jal
{\journalreference\jalname\elsevier}
\newcommand\jalprintyear
{\journalreferenceprintyear\jalname\elsevier}

\newcommand\jarname
{J. Automated Reasoning}
\newcommand\jar
{\journalreference\jarname\kluwer}
\newcommand\jarprintyear
{\journalreferenceprintyear\jarname\kluwer}

\newcommand\janclname{J. Applied Non-Classical Logics}
\newcommand\jancl{\journalreference\janclname?}

\newcommand\jcssname{J. Computer and System \Sci}
\newcommand\jcss
{\journalreference{\jcssname}\academicpress}
\newcommand\jcssprintyear
{\journalreferenceprintyear{\jcssname}\academicpress}

\newcommand\jlcname{J. Logic and Computation}
\newcommand\jlc
{\journalreference{\jlcname}\oxfordunipress}

\newcommand\jmathpuresapplname
{J.  de \Math\ Pures et Appliqu\'ees (J. \liouville)}

\newcommand\jmathpuresappl
{\journalreference{\jmathpuresapplname}?}

\newcommand\jphillogicname{J. Philosophical Logic}
\newcommand\jphillogic
{\journalreference{\jphillogicname}\kluwer}


\newcommand\jreineundangewandtemathematikname
{J.\ f\ue r die reine und angewandte Mathematik (\crelle sches J.)}

\newcommand\jreineundangewandtemathematik
{\journalreference{\jreineundangewandtemathematikname}?}


\newcommand\jscname
{J. Symbolic Computation}
\newcommand\jsc
{\journalreference{\jscname}\academicpress}
\newcommand\jscshort
{\journalreference{\jscname}?}
\newcommand\jscprintyear
%{\journalreferenceprintyear{\jscname}?}
{\journalreferenceprintyear{\jscname}\academicpress}

\newcommand\jslname{J. Symbolic Logic}
\newcommand\jsl
{\journalreference{\jslname}?}

\newcommand\leinseignementmathematiquename
{L'Enseignement Math\'e\-matique}
\newcommand\leinseignementmathematique
{\journalreference{\leinseignementmathematiquename}?}

\newcommand\linguisticinquiryname{Linguistic Inquiry}
\newcommand\linguisticinquiry
{\journalreference{\linguisticinquiryname}\mitpress}

\newcommand\linguisticsandphilosophyname{Linguistics and Philosophy}
\newcommand\linguisticsandphilosophy
{\journalreference{\linguisticsandphilosophyname}?}

\newcommand\ljigplname{Logic J. of the IGPL}
\newcommand\ljigpl
{\journalreference\ljigplname\oxfordunipress}
\newcommand\ljigplprintyear
{\journalreferenceprintyear\ljigplname\oxfordunipress}

\newcommand\logicauniversalisname{Logica Universalis}
\newcommand\logicauniversalis
{\journalreference\logicauniversalisname\birkhaeuser}

\newcommand\mathematicallogicquarterlyname{\Math\ Logic \Quart}
\newcommand\mathematicallogicquarterly
{\journalreference{\mathematicallogicquarterlyname}?}

\newcommand\mathematischezeitschrift
{\journalreference{Mathematische Zeitschrift}?}

\newcommand\mindname{Mind}

\newcommand\mind{\journalreference{\mindname}?}

\newcommand\MathematischeAnnalen{Mathe\-ma\-ti\-sche Annalen}
\newcommand\mathematischeannalen
{\journalreference{\MathematischeAnnalen}?}

\newcommand\mitteilungenmathgeshamburgprintyear
{\journalreferenceprintyear
{Mitteilungen der Mathematischen Gesellschaft in Hamburg}?}

\newcommand\modernlogic
{\journalreference{Modern Logic}?}

\newcommand\monatsheftempname
{Monat\esi hefte f\ue r Mathematik und Physik}

\newcommand\monatsheftemp
{\journalreference{\monatsheftempname}?}

\newcommand\NordiskMatematiskTidskrift
{\journalreference{Nordisk Matematisk Tidskrift}?}

\newcommand\notredamename{Notre Dame J. of Formal Logic}
\newcommand\notredame
{\journalreference{\notredamename}?}

\newcommand\philosphiamathname{Philosophia Mathematica (III)}
\newcommand\philosphiamath
{\journalreference{\philosphiamathname}?}

\newcommand\physisname{Physis}
\newcommand\physis{\journalreference{\physisname}?}

\newcommand\cambridgephilsoc
{\journalreference{\Proc\ \Cambridge\ Philosophical \Soc}?}

\newcommand\revuemetaphysiquemorale
{\journalreference{Revue de M\'etaphysique et de Morale}?}

\newcommand\sciencejournalname
{Science}

\newcommand\sciencejournalprintyear
{\journalreferenceprintyear{\sciencejournalname}?}

\newcommand\skriftername
{Skrifter, Norske Videnskaps-Akademi i Oslo 
(=  Videnskapsselskapet i Kristiania), 
Matema\-tisk-Natur\-viden\-skapelig Klasse}

\newcommand\skrifterpublisher
{J. Dybwad, \Oslo}

\newcommand\skrifter[4]
{\journalreference{\skriftername}
{\skrifterpublisher}{#1}{#1/#2}{#3}{#4}}

\newcommand\WarsawScientificSocietyIII
{Towarzystwa Naukowego Warszaw\-skiego, Wydzia\l\ III}

\newcommand\sprawozdaniazposiedzenname
{Sprawozdania z posiedze\'n \WarsawScientificSocietyIII\ (Comptes Rendus S\'eances Soci\'et\'e des Sciences et Lettres Varsovie, Cl.\,III)}

\newcommand\sprawozdaniazposiedzen
{\journalreference{\sprawozdaniazposiedzenname}?}

\newcommand\tcsname{Theoretical \CS}
\newcommand\tcsjournal
%{\journalreference\tcsname ?}
{\journalreference\tcsname\elsevier}
\newcommand\tcsjournalprintyear
%{\journalreference\tcsname ?}
{\journalreferenceprintyear\tcsname\elsevier}

\newcommand\themathematicsteachername{The Mathematics Teacher}
\newcommand\themathematicsteacher
{\journalreference{\themathematicsteachername}{ISSN\,0025-5769}}

\newcommand
\vierteljahresschriftfuerwissenschaftlichephilosophiename
{Vier\-tel\-jahr\esi schrift f\ue r wissenschaftliche Philosophie}

\newcommand\vierteljahresschriftfuerwissenschaftlichephilosophie
{\journalreference
{\vierteljahresschriftfuerwissenschaftlichephilosophiename}?}

\newcommand\ZLGname{Zeitschrift f\ue r \mathe\ Logik und Grundlagen der \Math}
\newcommand\ZLG
{\journalreference{\ZLGname}?}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ARCHIVES

\newcommand\handschrifenabteilungSUBGoettingen
{Nieder\-s\ae chsi\-sche Staat\es- und Universit\ae t\esi bibliothek 
 % of the {\namefont Georg August} Universit\ae t 
 \Goettingen, Hand\-schriften\-ab\-teilung}

\newcommand\handschriftenabteilungMIGoettingen
{Georg August Universit\ae t \Goettingen, 
 Mathematisches \Inst, Lesesaal}
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PROBLEMATIC URLS
\urldef\wirthkuhnurl\url
{http://wirth.bplaced.net/SEKI/welcome.html#SWP-2007-01}

\urldef\urlsrninetythreedashzerofive\url
{http://wirth.bplaced.net/SEKI/welcome.html#SR-93-05}

\urldef\urlsreightyeighttwelve\url
{http://wirth.bplaced.net/SEKI/welcome.html#SR-88-12}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
headernames.tex
\usepackage{amssymb}

\usepackage[T1]{fontenc}

% For teTeX distributions only:
\input specialfonts

% For texlive distributions only:
% \input newspecialfonts

\def\mathfrak#1{%
\mathchoice
{{\mfrak{#1}}}%                 display-style
{{\mfrak{#1}}}%                 text-style
{{\mscriptfrak{#1}}}%           scriptstyle
{{\mscriptscriptfrak{#1}}}%     scriptscriptstyle
}

\newcommand\mathfrakfootnote[1]{%
\mathchoice
{{\mfootnotefrak{#1}}}%               display-style
{{\mfootnotefrak{#1}}}%               text-style
{{\mscriptscriptscriptfrak{#1}}}%     scriptstyle
{{\mscriptscriptscriptfrak{#1}}}%     scriptscriptstyle
}

%\usepackage{ae,aecompl}

\input headernamesrest

headersugarterms.tex
\mathcommand\beginargs{(}
\mathcommand\allargs  {)}
\mathcommand\separgs  {,\,}
\mathcommand\tightsepargs{,}

\mathcommand\minusppnoparentheses  [2]{{#1}\,\minussymbol\,{#2}}
\mathcommand\tightminusppnoparentheses  [2]{{#1}\minussymbol{#2}}
\mathcommand\divideppnoparentheses [2]{{#1}\,\dividesymbol\,{#2}}
\mathcommand\plusppnoparentheses   [2]{{#1}\,\plussymbol \,{#2}}
\mathcommand\plusppnoparenthesesi  [3]{{#2}\,\plussymbol^{#1}\,{#3}}
\mathcommand\tightplusppnoparentheses   [2]{{#1}\plussymbol{#2}}
\mathcommand\timesppnoparentheses  [2]{{#1}\,\timessymbol\,{#2}}
\mathcommand\undppnoparentheses    [2]{{#1}\und            {#2}}
\mathcommand\oderppnoparentheses   [2]{{#1}\oder           {#2}}
\mathcommand\impliesppnoparentheses[2]{{#1}\implies        {#2}}
\mathcommand\leqinfixppnoparentheses[2]{{#1}\,\tight\leq\,{#2}}
\mathcommand\geqinfixppnoparentheses[2]{{#1}\,\tight\geq\,{#2}}
\mathcommand\dividepp [2]{(\divideppnoparentheses {#1}{#2})}
\mathcommand\minuspp  [2]{(\minusppnoparentheses  {#1}{#2})}
\mathcommand\pluspp   [2]{(\plusppnoparentheses   {#1}{#2})}
\mathcommand\timespp  [2]{(\timesppnoparentheses  {#1}{#2})}
\mathcommand\undpp    [2]{(\undppnoparentheses    {#1}{#2})}
\mathcommand\oderpp   [2]{(\oderppnoparentheses   {#1}{#2})}
\mathcommand\impliespp[2]{(\impliesppnoparentheses{#1}{#2})}


headertheorem.tex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\catcode`\@=11
%%%% added 3rd parameter being put to beginning of newtheorems text.
%       ****************************************
%       *         THEOREM ENVIRONMENTS         *
%       ****************************************
%
%  The user creates his own theorem-like environments with the command
%      \newtheorem{NAME}{TEXT}[COUNTER]  or
%      \newtheorem{NAME}[OLDNAME]{TEXT}
%  This defines the environment NAME to be just as one would expect a
%  theorem environment to be, except that it prints ``TEXT'' instead of
%  ``Theorem''.
%
%  If OLDNAME is given, then environments NAME and OLDNAME use the same
%  counter, so using a NAME environment advances the number of the next
%  NAME environment, and vice-versa.
%
%  If COUNTER is given, then environment NAME is numbered within COUNTER.
%  E.g., if COUNTER = subsection, then the first NAME in subsection 7.2
%  is numbered TEXT 7.2.1.
%
%  The way NAME environments are numbered can be changed by redefining
%  \theNAME.
%
%  DOCUMENT STYLE PARAMETERS
%
%  \@thmcounter{COUNTER} : A command such that
%               \edef\theCOUNTER{\@thmcounter{COUNTER}}
%         defines \theCOUNTER to produce a number for a theorem environment.
%         The default is:
%            BEGIN \noexpand\arabic{COUNTER} END
%
%  \@thmcountersep : A separator placed between a theorem number and
%         the number of the counter within which it is numbered.
%         E.g., to make the third theorem of section 7.2 be numbered
%         7.2-3, \@thmcountersep should be \def'ed to '-'.  Its
%         default is '.'.
%
%  \@begintheorem{NAME}{NUMBER} : A command that begins a theorem
%         environment for a 'theorem' named 'NAME NUMBER' --
%         e.g., \@begintheorem{Lemma}{3.7} starts Lemma 3.7.
%
%  \@opargbegintheorem{NAME}{NUMBER}{OPARG} : A command that begins a theorem
%         environment for a 'theorem' named 'NAME NUMBER' with optional
%         argument OPARG -- e.g., \@begintheorem{Lemma}{3.7}{Jones}
%         starts `Lemma 3.7 (Jones):'.
%
%  \@endtheorem : A command that ends a theorem environment.
%
% \newtheorem{NAME}{TEXT}[COUNTER] ==
%   BEGIN
%     if \NAME is definable
%       then \@definecounter{NAME}
%            if COUNTER present
%              then \@addtoreset{NAME}{COUNTER} fi
%                   \theNAME ==  BEGIN \theCOUNTER \@thmcountersep
%                                       eval\@thmcounter{NAME}      END
%              else \theNAME ==  BEGIN eval\@thmcounter{NAME} END
%            \NAME == \@thm{NAME}{TEXT}
%            \endNAME == \@endtheorem
%       else  error
%     fi
%   END
%
% \newtheorem{NAME}[OLDNAME]{TEXT}==
%   BEGIN
%     if \NAME is definable
%       then \theNAME == \theOLDNAME
%            \NAME == \@thm{OLDNAME}{TEXT}
%            \endNAME == \@endtheorem
%       else  error
%     fi
%   END
%
% \@thm{NAME}{TEXT} ==
%   BEGIN
%    \refstepcounter{NAME}
%    if next char = [
%       then \@ythm{NAME}{TEXT}
%       else \@xthm{NAME}{TEXT}
%    fi
%   END
%
% \@xthm{NAME}{TEXT} ==
%   BEGIN
%    \@begintheorem{TEXT}{\theNAME}
%    \ignorespaces
%   END
%
% \@ythm{NAME}{TEXT}[OPARG] ==
%   BEGIN
%    \@opargbegintheorem{TEXT}{\theNAME}{OPARG}
%    \ignorespaces
%   END
%
\def\newtheorem#1{\@ifnextchar[{\@othm{#1}}{\@nthm{#1}}}
 
\def\@nthm#1#2{%
%typical #1=definition, #2=Definition
\@ifnextchar[{\@xnthm{#1}{#2}}{\@ynthm{#1}{#2}}}
 
\def\@xnthm#1#2[#3]#4{%next line commented for brutal redefinition
%\expandafter\@ifdefinable\csname #1\endcsname
%typical #1=definition, #2=Definition, #3=section, #4=cpspecial
{\@definecounter{#1}\@addtoreset{#1}{#3}%
\expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand
  \csname the#3\endcsname \@thmcountersep \@thmcounter{#1}}%
\global\@namedef{#1}{\@thm{#1}{#2}{#4}}\global\@namedef{end#1}{\@endtheorem}}}
 
\def\@ynthm#1#2#3{%next line commented for brutal redefinition
%\expandafter\@ifdefinable\csname #1\endcsname
%typical #1=definition, #2=Definition, #3=cpspecial
{\@definecounter{#1}%
\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
\global\@namedef{#1}{\@thm{#1}{#2}{#3}}\global\@namedef{end#1}{\@endtheorem}}}
 
\def\@othm#1[#2]#3#4{%next line commented for brutal redefinition
%\expandafter\@ifdefinable\csname #1\endcsname
%typical #1=definition, #2=theorem, #3=Definition, #4=cpspecial
  {\global\@namedef{the#1}{\@nameuse{the#2}}%
\global\@namedef{#1}{\@thm{#2}{#3}{#4}}%
\global\@namedef{end#1}{\@endtheorem}}}
 
\def\@thm#1#2#3{\refstepcounter
    {#1}\@ifnextchar[{\@ythm{#1}{#2}{#3}}{\@xthm{#1}{#2}{#3}}}
 
\def\@xthm#1#2#3{\@begintheorem{#2}{\csname the#1\endcsname}{#3}\ignorespaces}
\def\@ythm#1#2#3[#4]{\@opargbegintheorem{#2}{\csname
       the#1\endcsname}{#4}{#3}\ignorespaces}
 
%DEFAULT VALUES
\def\@thmcounter#1{\noexpand\arabic{#1}}
\def\@begintheorem#1#2#3{\trivlist \item[\hskip \labelsep{\bf #1\ #2}]#3}
\def\@opargbegintheorem#1#2#3#4{\trivlist
      \item[\hskip \labelsep{\bf #1\ #2\ (#3)}]#4}
\def\@endtheorem{\endtrivlist}
 
%\def\@thmcountersep{}
%\newtheorem{theorem}            {Theorem}[thmcounter]{\mbox{}\it}
\def\@thmcountersep{.}
\def\globalrequirement{Global Requirement}

\newcommand\romanhelper{\hskip0.5em\mbox{}\rm}
\newtheorem{theorem}{Theorem}[section]{\mbox{}\it}
\newtheorem{lemma}     
[theorem]{Lemma}{\mbox{}\it}
\newtheorem{sublemma}  
[theorem]{Sublemma}{\mbox{}\it}
\newtheorem{corollary} 
[theorem]{Corollary}{\mbox{}\it}
\newtheorem{example}   
[theorem]{\Examplename}{\romanhelper}
\newtheorem{counterexample}   
[theorem]{Counterexample}{\romanhelper}
\newtheorem{exercise}   
[theorem]{Exercise}{\romanhelper}
\newtheorem{remark}    
[theorem]{Remark}{\romanhelper}
\newtheorem{forderung} 
[theorem]{\globalrequirement}{\mbox{}\it}
\newtheorem{requirement} 
[theorem]{Requirement}{\romanhelper}
\newtheorem{procedure}
[theorem]{Procedure}{\romanhelper}
\newtheorem{definition}
[theorem]{Definition}{\romanhelper}
\newtheorem{aufgabe}   
[theorem]{Aufgabe}{\romanhelper}
\newtheorem{specification}
[theorem]{Specification}{\romanhelper}
\newtheorem{problem}
[theorem]{Problem}{\romanhelper}
\newtheorem{axiom}
[theorem]{Axiom}{\romanhelper}
\catcode`\@=12

namedhelper.tex
\def\citep{\cite}
\def\citet#1{\citeauthor{#1} \shortcite{#1}}
\newcommand\startcite{{\raise.2ex\hbox{[}}}
\newcommand\stopcite {\raise.2ex\hbox{]}}
\newcommand\citehelper[1]{\startcite #1\stopcite}
\newcommand\makeaciteoftwo[2]
{\citehelper{\citeauthor{#1}, \citeyear{#1}; \citeyear{#2}}}
\newcommand\makeacitetoftwo[2]
{\citeauthor{#1} \citehelper{\citeyear{#1}; \citeyear{#2}}}
\newcommand\makeaciteofthree[3]
{\citehelper{\citeauthor{#1}, \citeyear{#1}; \citeyear{#2}; \citeyear{#3}}}
\newcommand\makeacitetofthree[3]
{\citeauthor{#1} \citehelper{\citeyear{#1}; \citeyear{#2}; \citeyear{#3}}}
\newcommand\makeaciteoffour[4]
{\citehelper{\citeauthor{#1}, \citeyear{#1}; \citeyear{#2}; \citeyear{#3};
\citeyear{#4}}}
\newcommand\makeacitetoffour[4]
{\citeauthor{#1} \citehelper{\citeyear{#1}; \citeyear{#2}; \citeyear{#3};
\citeyear{#4}}}
\newcommand\makeaciteoffive[5]
{\citehelper{\citeauthor{#1}, \citeyear{#1}; \citeyear{#2}; \citeyear{#3};
\citeyear{#4}; \citeyear{#5}}}
\newcommand\makeaciteofsix[6]
{\citehelper{\citeauthor{#1}, \citeyear{#1}; \citeyear{#2}; \citeyear{#3};
\citeyear{#4}; \citeyear{#5}; \citeyear{#6}}}
\newcommand\makeaciteofseven[7]
{\citehelper{\citeauthor{#1}, \citeyear{#1}; \citeyear{#2}; \citeyear{#3};
\citeyear{#4}; \citeyear{#5}; \citeyear{#6}; \citeyear{#7}}}
\newcommand\makeaciteofeight[8]
{\citehelper{\citeauthor{#1}, \citeyear{#1}; \citeyear{#2}; \citeyear{#3};
\citeyear{#4}; \citeyear{#5}; \citeyear{#6}; \citeyear{#7}; \citeyear{#8}}}
\newcommand\startacitewithnine[9]
{\startcite\citeauthor{#1}, \citeyear{#1}; 
\citeyear{#2}; \citeyear{#3}; \citeyear{#4}; \citeyear{#5};
\citeyear{#6}; \citeyear{#7}; \citeyear{#8}; \citeyear{#9};
}
\newcommand\stopacitewithone[1]{\citeyear{#1}\stopcite}
\newcommand\makeanextendedciteoftwo[4]
{\citehelper{\citeauthor{#2}, \citeyear{#2}, #1; \citeyear{#4}, #3}}
\newcommand\translationnotewithlongcite[3]{\cite[#1, #3]{#2}}

pdf.tex
%&latex

\newcommand\SEKImasterusepackages{\usepackage[T1]{fontenc}}
\typeout{CP's seki-example.tex,     Version 3.14, 2013/09/23}

\newcommand\SEKIusersusepackages
% Put all (!) your usepackage commands into the following block!
{%
\usepackage{graphicx}
\usepackage{named,makeidx}
\usepackage{amssymb}
\bibliographystyle{named}
\input namedhelper
\input dina4.sty
\input headerhot
\input headerforformulas
\input headersugarterms
\input headertheorem
}

\newcommand\SEKIREVIEWSTATUS{1}
% 0 No review. Only for edited volumes of reviewed papers.
%   Set \SEKISUBEDITOR to name of Editor!
% 1 Internal  review. Set \SEKIREVIEWER to name of reviewer.
% 2 External referee. Set \SEKIREFEREEPROCESS to name or institution of review.

\newcommand\SEKISUBEDITOR
{{\sc Erica Melis} 
\\FR Informatik, Universit\"at des Saarlandes, D--66123 Saarbr\"ucken, Germany
\\E-mail: {\tt melis@activemath.org}
\\WWW: \url{http://www.activemath.org/~melis}
}

\newcommand\SEKIREVIEWER
{\nedoname
\\The \wittgenstein\ Archive, 3 Anderson Court, Newnham Road, Cambridge, CB3 9EZ, England
\\E-mail: {\tt mn15@cam.ac.uk}
}

\newcommand\SEKIREFEREEPROCESS
{LPAR 2003, 
 10th International Conference on Logic for Programming,
 Artificial Intelligence, and Reasoning;
 full paper, 15 pp.
}

\newcommand\SEKIDOCUMENTCLASS{0}
% Set your LaTeX document class
% 0 article (preferred)
% 1 report (If you cant help!)

\newcommand\SEKIYEAR{2015}

\newcommand\SEKINUMBEROFYEAR{01}
% This should be two digits long at least

\newcommand\SEKITYPE{0}
% 0 seki report
% 1 seki working paper
% 2 Internet copy

\newcommand\SEKIPUBLISHEDTYPE{0}
% SYNOPSIS:
% 0 original
% 1 Published as \SEKIPUBLISHEDAS. For thesis.
% 2 The following publication is a short version of this report:
%   \SEKIPUBLISHEDAS
% 3 This report refines and extends the following publication:
%   \SEKIPUBLISHEDAS
%
% DESCRIPTION:
%
% The general idea is as follows: 
%
% \SEKIPUBLISHEDTYPE==0 is standard.
%
% If the original is at another place and
% your seki differs at most in typesetting, table of contents, index,
% \etc\ (as for a PhD or journal publication with limited copyright or
% availability), choose \SEKIPUBLISHEDTYPE==1.
%
% If you have a (short) version at a conference e.g. and you know 
% already about it, take \SEKIPUBLISHEDTYPE==2. %
%
% If you have a pre-version at a conference 
% already about it, take \SEKIPUBLISHEDTYPE==3. 


\newcommand\SEKIPUBLISHEDAS
{Master's thesis, 
 FR Informatik, Universit\"at des Saarlandes, D--66123 Saarbr\"ucken, Germany}
%
% One more example:
%
% \newcommand\SEKIPUBLISHEDAS{Serge Autexier, Carsten Sch\"urmann.
% {\em Disproving False Conjectures}.
%  Proceedings of the 10th International Conference on
%  Logic for
%  Programming,
%  Artificial Intelligence, and
%  Reasoning; Almaty, Kazakhstan.}
%\mediumfootroom 
% In case of \SEKIPUBLISHEDTYPE==0 this command is irrelevant,
% otherwise it writes something to the bottom line of the backside
% of the cover page as described above for \SEKIPUBLISHEDTYPE.

\title{\herbrandsfundamentaltheorem
\\---~an encyclopedia article~---} 
\author{\wirthnamenoindex\\\mbox{}\\\Institute\\\emailcp}

% Literally insert your macro files here please!
%
% NOTE: When you get name clashes without reasonable error messages,
%       to get possible more reasonable error messages,
%       insert the referred macros TEMPORARILY after \input seki-deckblatt-5
%       and \begin{document} 
\input seki-deckblatt-5
\input headernames
\date{\small Searchable Online Edition,
\\[+.4ex]Submitted \May\,24, 2014,
\\Revision Accepted \Mar\,4, 2015}
\newcommand\termsofdepth[2]{\app{{\mathcal T}_{#1}}{#2}}
\mathcommand\termsofdepthnovars[1]{{\mathcal T}_{#1}}
\mathcommand\termsofdepthnovarsstar[1]{{\mathcal T}_{#1}^*}
\newcommand\propertyC{\mbox{Property\hskip.2em C}} 
\renewcommand\namefont{\sc}
\newcommand\qed
{\relax\ifmmode\hskip2em \Box\else\unskip\nobreak\hskip1em $\Box$\fi}
\newcommand\existentialoid
{\math\gamma}\newcommand\existentialoidquantifier
{\mbox{\math\gamma-quantifier}}\newcommand\Anexistentialoidquantifier
{A \nolinebreak\existentialoidquantifier}\newcommand\anexistentialoidquantifier
{a \existentialoidquantifier}\newcommand
\Ruleofexistentialoidquantificationfirstpart
{Generalized rule of}\newcommand\Ruleofexistentialoidquantificationsecondpart
{\mbox{\math\gamma-quantification}}\newcommand
\Ruleofexistentialoidquantification
{\Ruleofexistentialoidquantificationfirstpart\
 \Ruleofexistentialoidquantificationsecondpart}\newcommand
\ruleofexistentialoidquantification
{generalized rule of \mbox{\math\gamma-quantification}}\newcommand
\Ruleofsimplificationfirstpart
{Generalized rule of}\newcommand\Ruleofsimplificationsecondpart
{simplification}\newcommand\Ruleofsimplification
{\Ruleofsimplificationfirstpart\ \Ruleofsimplificationsecondpart}\newcommand
\ruleofuniversaloidquantification
{generalized rule of \mbox{\math\delta-quantification}}\newcommand
\Ruleofuniversaloidquantificationfirstpart
{Generalized rule of}\newcommand
\Ruleofuniversaloidquantificationsecondpart
{\math\delta-quantification}\newcommand\Ruleofuniversaloidquantification
{\Ruleofuniversaloidquantificationfirstpart\ 
 \Ruleofuniversaloidquantificationsecondpart}\newcommand\universaloid
{\math\delta}\newcommand\universaloidquantifier
{\mbox{\math\delta-quantifier}}\newcommand\auniversaloidquantifier
{a \universaloidquantifier}
\begin{document}
\makecover
% Let your text start here, possibly changing the following a lot.
\maketitle
\begin{abstract}%
\sloppy
\herbrandsfundamentaltheorem\ provides a constructive characterization 
of derivability in first-order predicate logic by means of sentential logic.

Sometimes it is simply
called ``\herbrand's Theorem\closequotecomma but the longer name is
preferable as there are other important
``\herbrand\ theorems'' 
% (such as the {\herbrand--\ribet} Theorem)
and \herbrand\ himself called it\,{\em ``Th\'eor\`eme fondamental''}.

It was ranked by \citet{bernays-herbrand} as follows:
``In its proof-theoretic form,  
\herbrandindex\herbrand's Theorem can be seen
as the central theorem of predicate logic.
It expresses the relation of predicate logic to propositional logic
in a concise and felicitous form.'' 
And by 
\citet{heijenoort-logic-calculus-language}:
``Let me say simply, 
in conclusion,
that {\em\Begriffsschrift}~\cite{begriffsschrift},
\loewenheim's paper~\shortcite{loewenheim-1915},
and Chapter\,\,5 of \herbrand's thesis \shortcite{herbrand-PhD}
are the three cornerstones of modern logic.''

\herbrandsfundamentaltheorem\ occurs in \litchapref 5 of 
his \PhDthesis\ \shortcite{herbrand-PhD}
---~entitled {\em\herbrandPhDtitle}~--- 
submitted by \herbrandname\ \herbrandlifetime\ 
in\,1929 at the University of Paris.

\herbrandsfundamentaltheorem\ is, 
together with \goedel's incompleteness theorems
and \gentzensHauptsatz,
one of the most influential theorems
of modern logic.

Because of its complexity,
\herbrandsfundamentaltheorem\ is typically 
fouled up in textbooks beyond all recognition.
As we are convinced that 
there is still much more to learn for the future from this theorem than many 
logicians know,
we will focus on the true message and its practical impact.
This requires a certain amount of streamlining of \herbrand's work,
which will be compensated by some remarks on the actual historical facts.
\end{abstract}
\input body
\end{document}







seki-deckblatt-5.tex
% This file must not be modified!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

\typeout{CP's seki-deckblatt-5.tex, Version 3.15, 2013/08/19}
\typeout{ --- To be used for SEKIs since 2011 --- }

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\SEKIitemhelper{SEKI is published by the following institutions}
{German Research Center for Artificial Intelligence (DFKI GmbH), Germany\\[.5ex]
\begin{tabular}{l@{~}l@{}}
  $\bullet$&Robert Hooke Str.\,5, D--28359 Bremen
\\$\bullet$&Trippstadter Str.\,122, D--67663 Kaiserslautern
\\$\bullet$&Campus D~3~2, D--66123 Saarbr\"ucken
\\\end{tabular}
\\\\\\
% International University of Germany, Campus\,1, D--76646 Bruchsal, Germany
% \\\\
Jacobs University Bremen, School of Engineering \& Science, Campus Ring\,1, 
%\\\mbox{}\hfill 
D--28759 Bremen, Germany
\\\\
Universit\"at des Saarlandes, FR 6.2 Informatik, Campus, 
D--66123 Saarbr\"ucken, Germany}

\SEKIitemhelper{SEKI Editor}
{{\sc Claus-Peter Wirth}
\\E-mail: {\tt wirth@logic.at}
\\WWW: \url{http://wirth.bplaced.net}}

\SEKIitemhelper{Please send surface mail exclusively to}
{DFKI Bremen GmbH
\\Safe and Secure Cognitive Systems
\\Cartesium
\\Enrique Schmidt Str.\,5
\\D--28359 Bremen
\\Germany}
\vfill\vfill\vfill

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%typical #1=definition, #2=Definition
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{\@definecounter{#1}\@addtoreset{#1}{#3}%
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{\@definecounter{#1}%
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\catcode`\@=12

\newcommand\moreKeywords[2]{\vspace*{4ex}\par\noindent
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\newcommand\Keywords[1]{\moreKeywords{Keywords}{#1}}




specialfonts.tex
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% \sz\ may be more convenient, however. 


pdf.bbl
\begin{thebibliography}{}

\bibitem[\protect\citeauthoryear{Berka \bgroup\&\ \egroup
  Kreiser}{1973}]{logiktexte}
Karel Berka and Lothar Kreiser, editors.
\newblock {\em {Logik-Texte -- Kommentierte Au\esi wahl zur Geschichte der
  modernen Logik}}.
\newblock \akademieverlag, 1973.
\newblock \nth 2\,\rev\,\edn\ (\nth 1\,\edn\,1971; \nth
  4\,\rev\,\rev\,\edn\,1986).

\bibitem[\protect\citeauthoryear{Bernays{\protectedbernaysindex}}{1957}]{berna%
ys-herbrand}
Paul Bernays{\protectedbernaysindex}.
\newblock {\Ue ber den Zusammenhang des \herbrand schen Satzes mit den neueren
  Ergebnissen von \schuette{\protectedschuetteindex} und {\sc Stenius}}.
\newblock In {\em Proceedings of the International Congress of Mathematicians
  1954}, Groningen and Amsterdam, 1957. Noordhoff and \northholland.

\bibitem[\protect\citeauthoryear{Church}{1936}]{Church36b}
Alonzo Church.
\newblock A note on the {Entscheidung\esi problem}.
\newblock {\em \jslname}, 1:40--41,101--102, 1936.

\bibitem[\protect\citeauthoryear{Cohen \bgroup\&\ \egroup
  Wartofsky}{1967}]{boston-studies-3}
Robert~S. Cohen and Marx~W. Wartofsky, editors.
\newblock {\em {\Proc\ of the Boston Colloquium for the Philosophy of Science,
  1964--1966}: In Memory of {\namefont Norwood Russell Hanson}}.
\newblock Number~3 in Boston Studies in the Philosophy of Science.
  \DReidelpublishing, 1967.

\bibitem[\protect\citeauthoryear{Frege\protectedfregeindex}{1879}]{begriffssch%
rift}
Gottlob Frege\protectedfregeindex.
\newblock {\em {\Begriffsschrift, eine der arithmetischen nachgebildete
  Formelsprache de\es\ reinen Denken\es}}.
\newblock {Verlag von L. Nebert, \Halle}, 1879.
\newblock Corrected facsimile in \cite{begriffsschrift-und-andere}. \ Reprint
  of \PP{III}{VIII} and \PP{1}{54} in \cite[\PP{48}{106}]{logiktexte}. \
  {English} translation in \cite[\PP{1}{82}]{heijenoort-source-book}.

\bibitem[\protect\citeauthoryear{Frege\protectedfregeindex}{1964}]{begriffssch%
rift-und-andere}
Gottlob Frege\protectedfregeindex.
\newblock {\em {\Begriffsschrift\ und andere Auf\-s\ae tze}}.
\newblock \wissenschaftlichebuchgesellschaftdarmstadt, 1964.
\newblock {Zweite Au\fli age, mit \husserlname s und \scholzname' Anmerkungen,
  herau\esi gegeben von {\namefont Ignacio Angelelli}}.

\bibitem[\protect\citeauthoryear{Gabbay{\protectedgabbayindex} \bgroup\&\
  \egroup Woods}{2004\ff}]{handbook-of-the-history-of-logic}
Dov Gabbay{\protectedgabbayindex} and John Woods, editors.
\newblock {\em Handbook of the History of Logic}.
\newblock \northholland, 2004\ff.

\bibitem[\protect\citeauthoryear{Gentzen}{1935}]{gentzen}
Gerhard Gentzen.
\newblock {Untersuchungen \ue ber das logische Schlie\sz en}.
\newblock {\em Mathematische Zeitschrift}, 39:176--210,405--431, 1935.
\newblock Also in \cite[\PP{192}{253}]{logiktexte}. {English} translation in
  \cite{gentzen-collected}.

\bibitem[\protect\citeauthoryear{Gentzen}{1969}]{gentzen-collected}
Gerhard Gentzen.
\newblock {\em The Collected Papers of \gentzenname}.
\newblock {\northholland}, 1969.
\newblock \Ed\ by \szaboname.

\bibitem[\protect\citeauthoryear{Gillman}{1987}]{writing-mathematics}
Leonard Gillman.
\newblock {\em Writing Mathematics Well}.
\newblock The Mathematical Association of America, 1987.

\bibitem[\protect\citeauthoryear{G{\oe
  de{\protectedgoedelindex}l}}{1930}]{goedel-completeness}
Kurt G{\oe de{\protectedgoedelindex}l}.
\newblock {Die Vollst\ae ndigkeit der Axiome des logischen Funktionen\-kalk\ue
  ls}.
\newblock {\em {\monatsheftempname}}, 37:349--360, 1930.
\newblock With {English} translation also in \cite[\Vol\,I,
  \PP{102}{123}]{goedelcollected}.

\bibitem[\protect\citeauthoryear{G{\oe
  de{\protectedgoedelindex}l}}{1986ff.}]{goedelcollected}
Kurt G{\oe de{\protectedgoedelindex}l}.
\newblock {\em Collected Works}.
\newblock {\oxfordunipress}, 1986ff.
\newblock \Ed\ by \fefermanname, \dawsonname\protect\dawsonindex,
  \goldfarbname, \heijenoortname, \kleenename, \parsonsname, \siegname,
  \etalabbrev.

\bibitem[\protect\citeauthoryear{Goldfarb{\protectedgoldfarbindex}}{1970}]{rev%
iew-herbrand-ecrits-logiques}
Warren Goldfarb{\protectedgoldfarbindex}.
\newblock Review of \cite{herbrand-ecrits-logiques}.
\newblock {\em The Philosophical Review}, 79:576--578, 1970.

\bibitem[\protect\citeauthoryear{Heijenoort{\protectedheijenoortindex}}{1967}]%
{heijenoort-logic-calculus-language}
Jean~van Heijenoort{\protectedheijenoortindex}.
\newblock Logic as a calculus and logic as a language.
\newblock {\em Synthese}, 17:324--330, 1967.
\newblock Also in \cite[\PP{440}{446}]{boston-studies-3}. Also in
  \cite[\PP{11}{16}]{heijenoort-selected-essays}.

\bibitem[\protect\citeauthoryear{Heijenoort{\protectedheijenoortindex}}{1971}]%
{heijenoort-source-book}
Jean~van Heijenoort{\protectedheijenoortindex}.
\newblock {\em From {\frege} to {\namefont G\"odel}: A Source Book in
  Mathematical Logic, 1879--1931}.
\newblock {\harvardunipress}, 1971.
\newblock {\nth 2\,\rev\ \edn\ (\nth 1\,\edn\,1967)}.

\bibitem[\protect\citeauthoryear{Heijenoort{\protectedheijenoortindex}}{1975}]%
{heijenoort-herbrand}
Jean~van Heijenoort{\protectedheijenoortindex}.
\newblock \herbrand.
\newblock Unpublished typescript, \May\,18, 1975, \PPcount{15};
  \heijenoortname\ Papers, 1946--1988, Archives of American Mathematics, Center
  for American History, \unitexasaustin, Box\,3.8/86-33/1. \ Copy in
  \anellisarchives, 1975.

\bibitem[\protect\citeauthoryear{Heijenoort{\protectedheijenoortindex}}{1982}]%
{heijenoort-oeuvre-herbrand}
Jean~van Heijenoort{\protectedheijenoortindex}.
\newblock {L'\oefranz uvre} logique de {\herbrand} et son contexte historique.
\newblock 1982.
\newblock In \cite[\PP{57}{85}]{herbrand-symposium}. \Rev\ English translation
  is \cite{heijenoort-work-herbrand}.

\bibitem[\protect\citeauthoryear{Heijenoort{\protectedheijenoortindex}}{1986a}%
]{heijenoort-work-herbrand}
Jean~van Heijenoort{\protectedheijenoortindex}.
\newblock {\herbrand's} work in logic and its historical context.
\newblock 1986.
\newblock In \cite[\PP{99}{121}]{heijenoort-selected-essays}. \Rev\ English
  translation of \cite{heijenoort-oeuvre-herbrand}.

\bibitem[\protect\citeauthoryear{Heijenoort{\protectedheijenoortindex}}{1986b}%
]{heijenoort-selected-essays}
Jean~van Heijenoort{\protectedheijenoortindex}.
\newblock {\em Selected Essays}.
\newblock Bibliopolis, Napoli, copyright 1985. Also published by Librairie
  Philosophique J. Vrin, \Paris, 1986, 1986.

\bibitem[\protect\citeauthoryear{Heijenoort{\protectedheijenoortindex}}{1992}]%
{heijenoort-modern-logic}
Jean~van Heijenoort{\protectedheijenoortindex}.
\newblock Historical development of modern logic.
\newblock {\em Modern Logic}, 2:242--255, 1992.
\newblock Written in 1974.

\bibitem[\protect\citeauthoryear{Herbran{\protectedherbrandindex}d}{1930}]{her%
brand-PhD}
Jacques Herbran{\protectedherbrandindex}d.
\newblock {\em {\herbrandPhDtitle}}.
\newblock PhD thesis, Universit\'e de Paris, 1930.
\newblock {Th\`eses} pr\'esent\'ees \`a la facult\'e des Sciences de Paris pour
  obtenir le grade de docteur\`es sciences math\'ematiques --- \frenchnth 1
  \nolinebreak th\`ese: Recherches sur la th\'eorie de la d\'emonstration ---
  \frenchnth 2 \nolinebreak th\`ese: Propositions donn\'ees par la facult\'e,
  Les \'equations de Fredholm --- Soutenues le 1930 devant la commission
  d'examen --- Pr\'esident: M. \vessiot, Examinateurs: MM. {\namefont Denjoy,
  Frechet} --- Vu et approuv\'e, \Paris, le 20\,Juin\,1929, Le doyen de la
  facult\'e des Sciences, {\namefont C. Maurain} --- Vu et permis d'imprimer,
  \Paris, le 20\,Juin\,1929, Le recteur de l'Academie de \Paris, {\namefont S.
  Charlety} --- No.\,d'ordre\,2121, S\'erie\,A, No.\,de\,S\'erie\,1252 ---
  Imprimerie J. Dziewulski, Varsovie --- \Univ\ de \Paris. \ Also in Prace
  \WarsawScientificSocietyIII\ Nauk Matematyczno-Fizychnych, Nr.\,33,
  \Warszawa. \ A contorted, newly typeset reprint is
  \cite[\PP{35}{153}]{herbrand-ecrits-logiques}. \ Annotated {E}nglish
  translation {\em Investigations in Proof Theory}\/ by \goldfarbname\
  (\litchapfromtoref 1 4) and \drebenname\ and \heijenoortname\ (\litchapref 5)
  with a brief introduction by \goldfarb\ and extended notes by \goldfarb\
  \mbox{(\litnotefromtoref A C, K--M, O)}, \dreben\ (\litnotefromtoref F I),
  \dreben\ and \goldfarb\ (\litnoterefss D J N), and \dreben, \huffname, and
  \hailperinname\ (\litnoteref E) in
  \cite[\PP{44}{202}]{herbrand-logical-writings}. \ {E}nglish translation of
  \litsectref 5 with a different introduction by \heijenoort\ and some
  additional extended notes by \dreben\ also in
  \cite[\PP{525}{581}]{heijenoort-source-book}. \ \bibcrit{\herbrand's
  \PhDthesis, his cardinal work, dated \herbrandPhDdating; submitted at the
  \Univ\ of \Paris; defended at the Sorbonne \herbrandPhDdefensedate; printed
  in \WarszawaEnglish, 1930.}

\bibitem[\protect\citeauthoryear{Herbran{\protectedherbrandindex}d}{1968}]{her%
brand-ecrits-logiques}
Jacques Herbran{\protectedherbrandindex}d.
\newblock {\em {\'E}crits Logiques}.
\newblock Presses Universitaires de France, Paris, 1968.
\newblock Cortorted \edn~of \herbrand's logical writings by \heijenoortname.
  Review in \cite{review-herbrand-ecrits-logiques}. \hskip.2em {E}nglish
  translation is \cite{herbrand-logical-writings}.

\bibitem[\protect\citeauthoryear{Herbran{\protectedherbrandindex}d}{1971}]{her%
brand-logical-writings}
Jacques Herbran{\protectedherbrandindex}d.
\newblock {\em Logical Writings}.
\newblock {\harvardunipress}, 1971.
\newblock \Ed\ by \goldfarbname. Translation of \cite{herbrand-ecrits-logiques}
  with additional annotations, brief introductions, and extended notes by
  \goldfarb, \drebenname, and \heijenoortname. \
  \bibcrit{\textonherbrandlogicalwritings}.

\bibitem[\protect\citeauthoryear{Hilbe{\protectedhilbertindex}rt \bgroup\&\
  \egroup Ackermann\protect\ackermannindex}{1928}]{grundzuege}
David Hilbe{\protectedhilbertindex}rt and Wilhelm
  Ackermann\protect\ackermannindex.
\newblock {\em {Grundz\ue ge der theoretischen Logik}}.
\newblock Number XXVII in {Die Grundlehren der Mathematischen Wissenschaften in
  Einzeldarstellungen}. {\springerverlag}, 1928.
\newblock \nth 1\,\edn, the final version in a serious of three thorough
  revisions is \cite{grundzuege-vierte}.

\bibitem[\protect\citeauthoryear{Hilbe{\protectedhilbertindex}rt \bgroup\&\
  \egroup Ackermann\protect\ackermannindex}{1938}]{grundzuege-zweite}
David Hilbe{\protectedhilbertindex}rt and Wilhelm
  Ackermann\protect\ackermannindex.
\newblock {\em {Grundz\ue ge der theoretischen Logik}}.
\newblock Number XXVII in {Die Grundlehren der Mathematischen Wissenschaften in
  Einzeldarstellungen}. {\springerverlag}, 1938.
\newblock \nth 2\,\edn, most thoroughly revised edition of \cite{grundzuege}.
  {English} translation is \cite{grundzuege-zweite-english}.

\bibitem[\protect\citeauthoryear{Hilbe{\protectedhilbertindex}rt \bgroup\&\
  \egroup Ackermann\protect\ackermannindex}{1949}]{grundzuege-dritte}
David Hilbe{\protectedhilbertindex}rt and Wilhelm
  Ackermann\protect\ackermannindex.
\newblock {\em {Grundz\ue ge der theoretischen Logik}}.
\newblock Number~27 in {Die Grundlehren der Mathematischen Wissenschaften in
  Einzeldarstellungen}. {\springerverlag}, 1949.
\newblock \nth 3\,\edn, thoroughly revised edition of \cite{grundzuege-zweite}.

\bibitem[\protect\citeauthoryear{Hilbe{\protectedhilbertindex}rt \bgroup\&\
  \egroup Ackermann\protect\ackermannindex}{1950}]{grundzuege-zweite-english}
David Hilbe{\protectedhilbertindex}rt and Wilhelm
  Ackermann\protect\ackermannindex.
\newblock {\em {Grundz\ue ge der theoretischen Logik}}.
\newblock Chelsea, \NewYork, 1950.
\newblock English translation of \cite{grundzuege-zweite} by {\sc Lewis M.
  Hammond}, {\sc George G. Leckie}, and {\sc F. Steinhardt}, \ed\ and annotated
  by {\sc Robert E. Luce}. Reprinted by \AMSname\ 1999.

\bibitem[\protect\citeauthoryear{Hilbe{\protectedhilbertindex}rt \bgroup\&\
  \egroup Ackermann\protect\ackermannindex}{1959}]{grundzuege-vierte}
David Hilbe{\protectedhilbertindex}rt and Wilhelm
  Ackermann\protect\ackermannindex.
\newblock {\em {Grundz\ue ge der theoretischen Logik}}.
\newblock Number~27 in {Die Grundlehren der Mathematischen Wissenschaften in
  Einzeldarstellungen}. {\springerverlag}, 1959.
\newblock \nth 4\,\edn, most thoroughly revised and \extd\ edition of
  \cite{grundzuege-dritte}.

\bibitem[\protect\citeauthoryear{Hilbe{\protectedhilbertindex}rt \bgroup\&\
  \egroup
  Bernays{\protectedbernaysindex}}{1934}]{grundlagen-first-edition-volume-one}
David Hilbe{\protectedhilbertindex}rt and Paul Bernays{\protectedbernaysindex}.
\newblock {\em {Die Grundlagen der Mathematik --- Erster Band}}.
\newblock Number~XL in {Die Grundlehren der Mathematischen Wissenschaften in
  Einzeldarstellungen}. {\springerverlag}, 1934.
\newblock \nth 1\,\edn\ (\nth 2\,\edn\ is
  \cite{grundlagen-second-edition-volume-one}). English translation is
  \makeaciteoftwo{grundlagen-german-english-edition-volume-one-one}{grundlagen%
-german-english-edition-volume-one-two}.

\bibitem[\protect\citeauthoryear{Hilbe{\protectedhilbertindex}rt \bgroup\&\
  \egroup
  Bernays{\protectedbernaysindex}}{1968}]{grundlagen-second-edition-volume-one}
David Hilbe{\protectedhilbertindex}rt and Paul Bernays{\protectedbernaysindex}.
\newblock {\em {Die Grundlagen der Mathematik~I}}.
\newblock Number~40 in {Die Grundlehren der Mathematischen Wissenschaften in
  Einzeldarstellungen}. {\springerverlag}, 1968.
\newblock \nth 2\,\rev\,\edn\,of \cite{grundlagen-first-edition-volume-one}.
  English translation is
  \makeaciteoftwo{grundlagen-german-english-edition-volume-one-one}{grundlagen%
-german-english-edition-volume-one-two}.

\bibitem[\protect\citeauthoryear{Hilbe{\protectedhilbertindex}rt \bgroup\&\
  \egroup
  Bernays{\protectedbernaysindex}}{2015a}]{grundlagen-german-english-edition-v%
olume-one-one}
David Hilbe{\protectedhilbertindex}rt and Paul Bernays{\protectedbernaysindex}.
\newblock {\em {Grundlagen der Mathematik~I --- Foundations of Mathematics~I,
  Part\,A: \whatisinVolIPartA}}.
\newblock \url{http://wirth.bplaced.net/p/hilbertbernays}, 2015.
\newblock Thoroughly \rev\,\nth 3\,\edn\ (\nth 1\,\edn\ \collegepublications,
  2011). First English translation and bilingual facsimile \edn\ of the \nth 2
  German \edn\ \cite{grundlagen-second-edition-volume-one}, \incl\ the
  annotation and translation of all differences of the \nth 1 German \edn\
  \cite{grundlagen-first-edition-volume-one}. \ \Ed\ by \wirthname,
  \siekmannname, \michaelgabbayname, \gabbayname. \ Advisory Board: \siegname\
  (chair), \anellisname, \awodeyname, \baazname, \buchholzname, \buldtname,
  \kahlename, \mancosuname, \parsonsname, \peckhausname, \taitname, \tappname,
  \zachname. \ Translated and commented by \wirthname\ \etalabbrev.

\bibitem[\protect\citeauthoryear{Hilbe{\protectedhilbertindex}rt \bgroup\&\
  \egroup
  Bernays{\protectedbernaysindex}}{2015b}]{grundlagen-german-english-edition-v%
olume-one-two}
David Hilbe{\protectedhilbertindex}rt and Paul Bernays{\protectedbernaysindex}.
\newblock {\em {Grundlagen der Mathematik~I --- Foundations of Mathematics~I,
  Part\,B: \whatisinVolIPartB}}.
\newblock \url{http://wirth.bplaced.net/p/hilbertbernays}, 2015.
\newblock Thoroughly \rev\,\nth 3\,\edn. First English translation and
  bilingual facsimile \edn\ of the \nth 2 German \edn\
  \cite{grundlagen-second-edition-volume-one}, \incl\ the annotation and
  translation of all deleted texts of the \nth 1 German \edn\
  \cite{grundlagen-first-edition-volume-one}. \ \Ed\ by \wirthname,
  \siekmannname, \michaelgabbayname, \gabbayname. \ Advisory Board: \siegname\
  (chair), \anellisname, \awodeyname, \baazname, \buchholzname, \buldtname,
  \kahlename, \mancosuname, \parsonsname, \peckhausname, \taitname, \tappname,
  \zachname. \ Translated and commented by \wirthname\ \etalabbrev.

\bibitem[\protect\citeauthoryear{L{\"o}wenheim{\protectedloewenheimindex}}{191%
5}]{loewenheim-1915}
Leopold L{\"o}wenheim{\protectedloewenheimindex}.
\newblock {\Ue ber M\oe glich\-keiten im Relativ\-kalk\ue l}.
\newblock {\em {\MathematischeAnnalen}}, 76:228--251, 1915.
\newblock {English} translation {\em On Possibilities in the Calculus of
  Relatives} by \bauermengelbergname\ with an introduction by \heijenoortname\
  in \cite[\PP{228}{251}]{heijenoort-source-book}.

\bibitem[\protect\citeauthoryear{Smullyan}{1968}]{smullyan}
Raymond~M. Smullyan.
\newblock {\em First-Order Logic}.
\newblock {\springerverlag}, 1968.

\bibitem[\protect\citeauthoryear{Stern}{1982}]{herbrand-symposium}
Jacques Stern, editor.
\newblock {\em {\Proc\ of the \herbrand\ Symposium, Logic Colloquium'81,
  Marseilles, France, \Jul\,1981}}.
\newblock {\northholland}, 1982.

\bibitem[\protect\citeauthoryear{Turing}{1936/7}]{turing-entscheidungsproblem}
Alan~M. Turing.
\newblock On computable numbers, with an application to the {Entscheidung\esi
  problem}.
\newblock {\em Proceedings of the London Mathematical Society, Ser.\,2},
  42:230--265, 1936/7.
\newblock Received \May\,28, 1936\@. Correction in
  \cite{turing-entscheidungsproblem-correction}.

\bibitem[\protect\citeauthoryear{Turing}{1937}]{turing-entscheidungsproblem-co%
rrection}
Alan~M. Turing.
\newblock On computable numbers, with an application to the {Entscheidung\esi
  problem}. {A} correction.
\newblock {\em Proceedings of the London Mathematical Society, Ser.\,2},
  43:544--546, 1937.
\newblock Correction of \cite{turing-entscheidungsproblem} according to the
  errors found by \bernaysname.

\bibitem[\protect\citeauthoryear{Whitehead{\protect\whiteheadindex} \bgroup\&\
  \egroup Russe{\protectedrussellindex}ll}{1910--1913}]{PM}
Alfred~North Whitehead{\protect\whiteheadindex} and Bertrand
  Russe{\protectedrussellindex}ll.
\newblock {\em Principia Mathematica}.
\newblock {\cambridgeunipress}, 1910--1913.
\newblock {\nth 1\,\edn}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}
  \bgroup\&al.\egroup }{2009}]{herbrand-handbook}
Claus-Peter Wirth{\protectedwirthindex}, J{\"o}rg Siek{\-}mann,
  {\mbox{Ch}}ristoph Benz{\-}m{\ue}ller{\protectedbenzmuellerindex}, and Serge
  Autexier{\protectedautexierindex}.
\newblock \herbrandname: Life, logic, and automated deduction.
\newblock 2009.
\newblock In \cite[\Vol\,5: Logic from \russell\ to \church,
  \PP{195}{254}]{handbook-of-the-history-of-logic}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}
  \bgroup\&al.\egroup }{2014}]{SR--2009--01}
Claus-Peter Wirth{\protectedwirthindex}, J{\"o}rg Siek{\-}mann,
  {\mbox{Ch}}ristoph Benz{\-}m{\ue}ller{\protectedbenzmuellerindex}, and Serge
  Autexier{\protectedautexierindex}.
\newblock {\em Lectures on {\herbrandname} as a Logician}.
\newblock {SEKI-Report SR--2009--01 (ISSN 1437--4447)}. {SEKI Publications},
  2014.
\newblock \Rev\,\edn\ \May\,2014, \PPcount{ii+82},
  {\url{http://arxiv.org/abs/0902.4682}}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{2012}]{wirth-hei%
jenoort}
Claus-Peter Wirth{\protectedwirthindex}.
\newblock {\herbrandsfundamentaltheorem} in the eyes of {\heijenoortname}.
\newblock {\em {\logicauniversalisname}}, 6:485--520, 2012.
\newblock Received \Jan\,12, 2012. Published online \Jun\,22, 2012,
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\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{2014}]{wirth-hei%
jenoort-SEKI}
Claus-Peter Wirth{\protectedwirthindex}.
\newblock {\em {\herbrandsfundamentaltheorem:} The Historical Facts and their
  Streamlining}.
\newblock {SEKI-Report SR--2014--01 (ISSN 1437--4447)}. {SEKI Publications},
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\newblock \PPcount{ii+47}, \url{http://arxiv.org/abs/1405.6317}.

\end{thebibliography}
