- 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*& F*x*)). 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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