axiom of power set

Definitions

1. 1

   The axiom that the power set of any set exists and is a valid set, which appears in the…

   The axiom that the power set of any set exists and is a valid set, which appears in the standard axiomatisation of set theory, ZFC.

   • The axiom of choice differs from other axioms of ZF by stating existence of a set (i.e., a choice function) without defining it (unlike, for instance, the axiom of pairing or the axiom of power set).
   • Verifying that the axiom of power set is in #92;#123;#92;phi#92;in#92;mathcal#123;L#125;#42;#58;S#92;vdash#92;mathcal#123;I#125;(#92;phi)#92;#125; relies on some rudimentary comprehension axioms.
   • But the ZF axioms of which the hierarchy is an intuitive model involve impredicative quantifications. Most striking is the axiom of power set in tandem with the axiom of separation.

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