  This thesis presents an alternative to Cantor's theory of cardinality,
insofar as that is understood as a theory of set size.
  The alternative is based on a general theory, ClassSize. ClassSize contains
all sentences in the first order language with "subset" and "smaller-than"
predicates which are true in all finite power sets.
  ClassSize is decidable but not finitely axiomatizable.
  Every infinite completion of ClassSize has a model over the power set of the
natural numbers which satisfies an additional axiom, OUTPACING: If initial
segments of A eventually become smaller than the corresponding initial segments
of B, then A is smaller than B.
  Models which satisfy OUTPACING seem to accord with common intuitions about
set size. In particular, they agree with the ordering suggested by the notion
of "asymptotic density".
