Definition:Zermelo-Fraenkel Axioms

The Zermelo-Fraenkel axioms are the most well-known basis for axiomatic set theory.

There is no standard numbering for them, and their exact formulation varies. Certain axioms can in fact be derived from other axioms, so their status as "axioms" can be questioned.

The axioms are as follows:

The Axiom of Foundation
In addition to the above axioms, there is a further axiom which is still hotly debated as to its validity: