Domain Axiom for classes

The Domain Axiom is a possible axiom of Material set theory with classes¹:

(\forall ℭ 𝔩 𝔰 𝑋) (\exists ℭ 𝔩 𝔰 𝑍) (\forall 𝑢) [𝑢 \in 𝑍 ⟺ (\exists 𝑣) [(𝑢, 𝑣) \in 𝑋]]

which is to say, the domain of any Relation set $𝑋$ exists, unique by extensionality, and denoted $d o m 𝑋$ .

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

Footnotes