Set Theories

https://en.wikipedia.org/wiki/Set_theory https://en.wikipedia.org/wiki/Naive_set_theory https://en.wikipedia.org/wiki/Axiomatic_system https://en.wikipedia.org/wiki/Axiom 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)