Answer by Joel David Hamkins for Is the universe of ZFA rigid? The pairing...
You have answered your own question.In ZFA, every definable permutation $\pi:A\to A$ of the class of atoms extends uniquely to an automorphism of the entire set-theoretic universe, simply by defining...
View ArticleIs the universe of ZFA rigid? The pairing axiom implies that even atoms have...
Although any permutation of atoms induces an automorphism of the whole universe, atoms seem to be indiscernible only within the permutation models. Can a permutation model be extended to a rigid...
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