Material set theory

Domain Axiom for classes

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

(∀ℭ𝔩𝔰⁡𝑋)(∃ℭ𝔩𝔰⁡𝑍)(∀𝑢)[𝑢∈𝑍⟺(∃𝑣)[(𝑢,𝑣)∈𝑋]]

which is to say, the domain of any Relation set 𝑋 exists, unique by extensionality, and denoted dom⁡𝑋.

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Footnotes

1. 2015. Introduction to Mathematical Logic, §4.1, p. 235 ↩