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{{Short description|Model of set theory constructed using permutations}}
In mathematical [[set theory]], a '''permutation model''' is a [[model (mathematical logic)|model]] of set theory with [[Atom (set theory)|atoms]] (ZFA) constructed using a [[permutation group|group]] of [[permutation]]s of the atoms. A '''symmetric model''' is similar except that it is a model of ZF (without atoms) and is constructed using a group of permutations of a forcing [[poset]]. One application is to show the independence of the [[axiom of choice]] from the other axioms of ZFA or ZF.
Permutation models were introduced by {{harvs|txt|last=Fraenkel|year=1922}} and developed further by {{harvs|txt|last=Mostowski|year=1938}}.
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