separation, axiom of

separation, axiom of
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.

Philosophy dictionary. . 2011.

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