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Line 1: In mathematical set theory, a '''permutation model''' is a model of set theory with atoms (ZFA) constructed using a group of permutations of the atoms. Permutation models were introduced by {{harvs\|txt\|last=Fraenkel\|year=1922}} and developed further by {{harvs\|txt\|last=Mostowski\|year=1938}}. One application is to show the independence of the [[axiom of choice]] from various other axioms in set theory with atoms. Paul COhen leter used similar ideas to construct models of ZF not satisfying the axiom of choice, by replacing a group acting on a set of atoms by a group acting on a forcing poset. ==Construction of permutation models==

Permutation model: Difference between revisions