# Set Theories

[https://en.wikipedia.org/wiki/Set\_theory](https://en.wikipedia.org/wiki/Set_theory) [https://en.wikipedia.org/wiki/Naive\_set\_theory](https://en.wikipedia.org/wiki/Naive_set_theory) [https://en.wikipedia.org/wiki/Axiomatic\_system](https://en.wikipedia.org/wiki/Axiomatic_system) [https://en.wikipedia.org/wiki/Axiom](https://en.wikipedia.org/wiki/Axiom) [https://en.wikipedia.org/wiki/Axiom\_schema](https://en.wikipedia.org/wiki/Axiom_schema)

## Axiomatic set theories

* Naive Set Theory
* Axiomatic Set Theory
* Theory of Types: Russell and Whitehead
* New Foundations (NF): 1937 by Quine, simplification of the type theory
* Mathematical Logic (ML): 1940, Quine's extension of NF, includes classes
* Morse-Kelley set theory (MK)
* von Neumann-Bernays-Gödel Set Theory (NBG)
* Zermelo's set theory
* Zermelo-Fraenkel set theory (ZF)
* Zermelo-Fraenkel set theory with axiom of choice (ZFC)
* Kripke-Platek set theory
* General set theory that Burgess (2005) calls "ST"
* Church's set theory CUS
* Positive Set Theory (studied by the School around Roland Hinnion at the Universite Libre de Bruxelles)
