Condensable models of set theory

Ali Enayat

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arXiv · 1910.04029

Condensable models of set theory

Ali Enayat

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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.

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BibTeX RIS

Ali Enayat. 2019-10-09. Condensable models of set theory. https://arxiv.org/abs/1910.04029

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