- Source: List of alternative set theories
In mathematical logic, an alternative set theory is any of the alternative mathematical approaches to the concept of set and any alternative to the de facto standard set theory described in axiomatic set theory by the axioms of Zermelo–Fraenkel set theory.
Alternative set theories
Alternative set theories include:
Vopěnka's alternative set theory
Von Neumann–Bernays–Gödel set theory
Morse–Kelley set theory
Tarski–Grothendieck set theory
Ackermann set theory
Type theory
New Foundations
Positive set theory
Internal set theory
Pocket set theory
Naive set theory
S (set theory)
Double extension set theory
Kripke–Platek set theory
Kripke–Platek set theory with urelements
Scott–Potter set theory
Constructive set theory
Zermelo set theory
General set theory
See also
Non-well-founded set theory
List of first-order theories § Set theories
Notes
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- List of alternative set theories
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- Zermelo–Fraenkel set theory
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- Ackermann set theory
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