> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/900-index/enums/enum-axioms/axioms-per-theory/axioms-in-zf.md).

# 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