ZF + “Every set is the same size as a wellfounded set”
Forster, Thomas
J. Symbolic Logic, Tome 68 (2003) no. 1, p. 1-4 / Harvested from Project Euclid
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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.
Publié le : 2003-03-14
Classification:  
@article{1045861502,
     author = {Forster, Thomas},
     title = {ZF + ``Every set is the same size as a wellfounded set''},
     journal = {J. Symbolic Logic},
     volume = {68},
     number = {1},
     year = {2003},
     pages = { 1-4},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1045861502}
}

Forster, Thomas. ZF + “Every set is the same size as a wellfounded set”. J. Symbolic Logic, Tome 68 (2003) no. 1, pp.  1-4. http://gdmltest.u-ga.fr/item/1045861502/