Powerset Axiom

The Powerset Axiom is a possible axiom of Material set theory asserting the existence of the powerset: #m/def/set/zf

(\forall 𝔐 𝐴) [\exists 𝔐 𝑃] (𝑋 \in 𝑃 ⟺ 𝔐 (𝑋) \land 𝑋 \subseteq 𝐴)

where $𝑋 \subseteq 𝐴$ denotes subset, which is to say, for any set $𝐴$ there exists a set of all its subsets $𝑃$ , which by the Axiom of Extensionality is unique and we denote $P (𝐴)$ and call the powerset.

#state/tidy | #lang/en | #SemBr