Material set theory

Universal Relation Axiom

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

(โˆ€โ„ญ๐”ฉ๐”ฐโก๐‘‹)(โˆƒโ„ญ๐”ฉ๐”ฐโก๐‘)(โˆ€๐‘ข)(โˆ€๐‘ฃ)[(๐‘ข,๐‘ฃ)โˆˆ๐‘โŸบ๐‘ขโˆˆ๐‘‹]

which is to say, for any class ๐‘‹ there is a class representing a Relation set between each element of ๐‘‹ and everything else in the universal class, a sort of โ€œCartesian productโ€ ๐‘‹ ร—๐‘‰.


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

Footnotes

  1. 2015. Introduction to Mathematical Logic, ยง4.1, p. 236, B5 โ†ฉ