  We call a subset of an ordinal $\lambda$ recognizable if it is the unique
subset $x$ of $\lambda$ for which some Turing machine with ordinal time and
tape, which halts for all subsets of $\lambda$ as input, halts with the final
state $0$. Equivalently, such a set is the unique subset $x$ which satisfies a
given $\Sigma_1$ formula in $L[x]$. We prove several results about sets of
ordinals recognizable from ordinal parameters by ordinal time Turing machines.
Notably we show the following results from large cardinals.
  (1) Computable sets are elements of $L$, while recognizable objects with
infinite time computations appear up to the level of Woodin cardinals.
  (2) A subset of a countable ordinal $\lambda$ is in the recognizable closure
for subsets of $\lambda$ if and only if it is an element of $M^{\infty}$, where
$M^{\infty}$ denotes the inner model obtained by iterating the least measure of
$M_1$ through the ordinals, and where the recognizable closure for subsets of
$\lambda$ is defined by closing under relative recognizability for subsets of
$\lambda$.
