Material set theory

Universal Relation Axiom

The Universal Relation Axiom is a possible axiom of Material set theory with classes¹: nbg

(∀ℭ𝔩𝔰⁡𝑋)(∃ℭ𝔩𝔰⁡𝑍)(∀𝑢)(∀𝑣)[(𝑢,𝑣)∈𝑍⟺𝑢∈𝑋]

which is to say, for any class 𝑋 there is a class representing a Relation set between each element of 𝑋 and everything else in the universal class, a sort of “Cartesian product” 𝑋 ×𝑉.

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tidy | en | SemBr

Footnotes

1. 2015. Introduction to Mathematical Logic, §4.1, p. 236, B5 ↩