[[Set theory MOC]]
# Zermelo-Fraenkel set theory

**Zermelo-Fraenkel set theory** or $\mathrm{ZF}$ is a [[Material set theory]] and the most widely accepted [[Axiomatic set theory]] (together with the stronger [[ZFC]]).

## Axioms

We take the following axioms and axiom schemata: #m/def/set/zf 

1. [[Axiom of Extensionality]]
2. [[Emptyset Axiom]]
3. [[Axiom of Pairing]]
4. [[Axiom of Union]]
5. [[Specification Axiom Schema]]
6. [[Powerset Axiom]]
7. [[Axiom of Infinity]]
8. [[Axiom Schema of Replacement]]
9. [[Axiom of Foundation]]


  [^2006]: 2006\. [[Sources/@moschovakisNotesSetTheory2006|Notes on set theory]], pp. 23ff

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