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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
Subject categories Logic, Algebra and Logic


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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