Sets and Their Sizes
| dc.creator | Katz, Fred M. | |
| dc.date | 2001-06-13 | |
| dc.date.accessioned | 2026-07-07T04:42:07Z | |
| dc.date.available | 2026-07-07T04:42:07Z | |
| dc.description | 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". | |
| dc.identifier | https://arxiv.org/abs/math/0106100 | |
| dc.identifier | http://arxiv.org/abs/math/0106100 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61643 | |
| dc.subject | Logic | |
| dc.subject | 03E10; 54A25 | |
| dc.title | Sets and Their Sizes | |
| dc.type | text |