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

(∀𝔐⁡𝐴)[∃𝔐⁡𝑃](𝑋∈𝑃⟺𝔐⁡(𝑋)∧𝑋⊆𝐴)

where 𝑋 ⊆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