Zermelo-Fraenkel Set Theory

Last updated Nov 1, 2022

1. Axiom of Extensionality
2. Axiom of Regularity
3. Axiom Schema of Specification
4. Axiom of Pairing
5. Axiom of Union
6. Axiom Schema of Replacement
7. Axiom of Infinity
8. Axiom of Power Set
9. *Axiom of Choice

1. Axioms (1)-(8) form ZF-Theory. Together with Axiom (9) we get ZFC-Theory.
2. See Axiom of Choice for equivalent statements.