- 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 )((x ∈ y ) iff (x ∈z & 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. Academic. 2011.
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