Set Theory/Zermelo‒Fraenkel set theory

< Set Theory

Definition (Zermelo‒Fraenkel set theory):

Zermelo‒Fraenkel set theory is the theory given by the following axioms:

Axiom of extensionality: $\forall x,y:x=y\Leftrightarrow (z\in x\Leftrightarrow z\in y)$
Empty set: $\exists \emptyset :\forall x:x\notin \emptyset$
Pairing:
Union:
Power set:
Regularity:
Infinity:
Comprehension:

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