Material set theory

Axiom of Pairing

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

which is to say, for any two objects (possibly the same) there is a set whose only elements are those two objects. It follows from the Axiom of Extensionality that such a doubleton is unique, which we denote .

Axiom of Pairing for classes

In a material set theory with classes, we must modify the axiom slightly, since we cannot pair proper classes: #m/def/set/nbg

#state/develop | #lang/en | #SemBr