ZF + "every set is the same size as a wellfounded set"

Journal of Symbolic Logic 68 (1):1-4 (2003)
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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 formulæ. The class of models of ZFB is closed under creation of Rieger-Bernays permutation models

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10.2178/jsl/1045861502

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Thomas Forster
Cambridge University

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Permutations and stratified formulae a preservation theorem.Thomas Forster - 1990 - Mathematical Logic Quarterly 36 (5):385-388.
Permutations and stratified formulae a preservation theorem.Thomas Forster - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (5):385-388.

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