Condensable models of set theory
Logic
2021-06-21 v4
Abstract
We study models M of set theory that are "condensable", in the sense that there is an "ordinal" v of M such that the rank initial segment of M determined by v is both isomorphic to M, and also an elementary submodel of M for infinitary formulae in the well-founded part of M. We prove, assuming a modest set theoretic hypothesis, that there are condensable models M of ZFC such that every definable element of M is in the well-founded part of M. We also provide various characterizations of countable condensable models of ZF.
Keywords
Cite
@article{arxiv.1910.04029,
title = {Condensable models of set theory},
author = {Ali Enayat},
journal= {arXiv preprint arXiv:1910.04029},
year = {2021}
}
Comments
15 pages (this is revised version of a previously posted draft)