[[Material set theory]]
# Powerset Axiom

The **Powerset Axiom** is a possible axiom of [[Material set theory]] asserting the existence of the [[powerset]]: #m/def/set/zf 
$$
\begin{align*}
(\forall\shood A)[\exists \shood P](X \in P \iff \shood(X) \land X \sube A)
\end{align*}
$$
where $X \sube A$ 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 $\mathcal{P}(A)$ and call the [[powerset]].


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