# Axiom of power set

## Concept in axiomatic set theory / From Wikipedia, the free encyclopedia

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In mathematics, the **axiom of power set**^{[1]} is one of the Zermelo–Fraenkel axioms of axiomatic set theory. It guarantees for every set $x$ the existence of a set ${\mathcal {P}}(x)$, the power set of $x$, consisting precisely of the subsets of $x$. By the axiom of extensionality, the set ${\mathcal {P}}(x)$ is unique.

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The axiom of power set appears in most axiomatizations of set theory. It is generally considered uncontroversial, although constructive set theory prefers a weaker version to resolve concerns about predicativity.