# Condensable models of set theory

**Authors:** Ali Enayat  
**arXiv:** [1910.04029](https://arxiv.org/abs/1910.04029)  
**Date:** 2019-10-09  
**Summary page:** https://www.summarizepaper.com/fr/paper/1910.04029v4/

## 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.