Material set theory Powerset Axiom The Powerset Axiom is a possible axiom of Material set theory asserting the existence of the powerset: zf (βπβ‘π΄)[βπβ‘π](πβπβΊπβ‘(π)β§πβπ΄) where π βπ΄ denotes subset, which is to say, for any set π΄ there exists a set of all its subsets π, which by the Axiom of Extensionality is unique and we denote P(π΄) and call the powerset. tidy | en | SemBr