# ZF Axioms

* `ZF` - the Zermelo-Fraenkel set theory without the axiom of choice
* `ZFC` - the Zermelo-Fraenkel set theory with the axiom of choice

Together with the axiom of choice, these are the de facto standard axioms for contemporary mathematics or set theory.

ZF axioms:

* Axiom of extensionality
* Axiom of empty set
* Axiom of pairing
* Axiom of union
* Axiom of infinity
* Axiom schema of replacement
* Axiom of power set
* Axiom of regularity
* Axiom schema of specification