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Incurvati, Luca
2020.
Conceptions of Set and the Foundations of Mathematics.
Published online by Cambridge University Press: 12 March 2014
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.