Material set theory

Axiom of Union

The Axiom of Union is a possible axiom of Material set theory: #m/def/set/zf

which is to say, for any set there exists a union consisting of the elements of the elements of . It follows from the Axiom of Extensionality that such a is unique, and we denote it by .

In a material set theory with classes like , the existence of a union class is already guaranteed by other axioms, but one requires the above axiom to guarantee that the union of sets is itself a set.

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