One of the Zermelo-Fraenkel axioms which asserts the existence for any set a of the power set x consisting of all the subsets of a. The axiom may be stated symbolically as for all x exists y( for all z(z element y congruent z subset x)) (Enderton 1977). Note that the version given by Itô, for all x exists y(y element x congruent for all z element y(z element a)), is confusing, and possibly incorrect.
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