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Condensable models of set theory

Working paper
Authors Ali Enayat
Publication year 2019
Published at Department of Philosophy, Linguistics and Theory of Science
Language en
Links https://arxiv.org/abs/1910.04029
Subject categories Logic, Algebra and Logic

Abstract

We study models M of set theory that are "condensable", in the sense that there is an "ordinal" o of M such that the rank initial segment of M determined by o 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 a structural characterization of condensable models of ZF.

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