Definition:Zermelo-Fraenkel Set Theory

Definition
Zermelo-Fraenkel Set Theory is a system of axiomatic set theory upon which the whole of (at least conventional) mathematics can be based.

Its basis consists of a system of Aristotelian logic, appropriately axiomatised, together with the Zermelo-Fraenkel axioms of set theory.

These are as follows:

Also known as
Zermelo-Fraenkel set theory is often seen abbreviated as ZF.

Also see

 * Definition:ZFC, which is Zermelo-Fraenkel set theory with the addition of the axiom of choice