axiom of separation

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Also known as the Aussonderungsaxiom. The unrestricted principle of comprehension leads to contradiction in set theory. The axiom of separation, due to Zermelo, restored consistency by allowing a set of objects to exist when it is the subset of a previous set, and its members meet a condition: (∃y)(∀x)(xy) iff (xz & Fx). That is, a set y of objects exists when it is separated out from a previously given set z, as the subset whose members meet a condition F.

Subjects: Philosophy.

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