Definition:Axiomatic Set Theory

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Axiomatic set theory is a system of set theory which differs from so-called naive set theory in that the sets which are allowed to be generated are strictly constrained by the axioms.

The best known systems of axiomatic set theory are ZF (Zermelo-Fraenkel) and ZFC (Zermelo-Fraenkel with the Axiom of Choice).

Also see

  • Results about axiomatic set theory can be found here.