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
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
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