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March 2003 ZF + “Every set is the same size as a wellfounded set”
Thomas Forster
J. Symbolic Logic 68(1): 1-4 (March 2003). DOI: 10.2178/jsl/1045861502

Abstract

Let ZFB be ZF + “every set is the same size as a wellfounded set”. Then the following are true.

Every sentence true in every (Rieger-Bernays) permutation model of a model of ZF is a theorem of ZFB. (i.e., ZFB is the theory of Rieger-Bernays permutation models of models of ZF)

ZF and ZFAFA are both extensions of ZFB conservative for stratified formul{\ae}.

{The class of models of ZFB is closed under creation of Rieger-Bernays permutation models.

Citation

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Thomas Forster. "ZF + “Every set is the same size as a wellfounded set”." J. Symbolic Logic 68 (1) 1 - 4, March 2003. https://doi.org/10.2178/jsl/1045861502

Information

Published: March 2003
First available in Project Euclid: 21 February 2003

zbMATH: 1044.03037
MathSciNet: MR1959308
Digital Object Identifier: 10.2178/jsl/1045861502

Rights: Copyright © 2003 Association for Symbolic Logic

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Vol.68 • No. 1 • March 2003
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