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)

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