Zermelo-Fraenkel
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In mathematics, Zermelo-Fraenkel set theory (ZFC) is the standard formal axiomatization of axiomatic set theory. It is commonly considered the foundation of modern mathematics.[1] It was formulated by two logicians, Zermelo and Fraenkel.
The axioms include the Axiom of Choice, however mathematicians who find this axiom questionable often replace it with the more sound Axiom of Determinacy.
The nine axioms in Zermelo-Fraenkel set theory are:
- Axiom of Empty Set
- Axiom of Extensionality
- Axiom of Unordered Pairing
- Axiom of Subset
- Axiom of Superset
- Axiom of Power
- Axiom of Infinity
- Axiom of Replacing
- Axiom of Foundation
- Axiom of Choice