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 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
Mathematicians who find the Axiom of Choice, however this axiom questionable often replace it with the more sound Axiom of Determinacy.