Journal of Symbolic Logic

ZF + “Every set is the same size as a wellfounded set”

Thomas Forster

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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.

Article information

J. Symbolic Logic, Volume 68, Issue 1 (2003), 1-4.

First available in Project Euclid: 21 February 2003

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Forster, Thomas. ZF + “Every set is the same size as a wellfounded set”. J. Symbolic Logic 68 (2003), no. 1, 1--4. doi:10.2178/jsl/1045861502.

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