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