# Definition:Axiomatic Set Theory

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## Definition

**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.

## Sources

- 1972: Patrick Suppes:
*Axiomatic Set Theory*(2nd ed.) ... (next): Preface to the First Edition - 2010: Raymond M. Smullyan and Melvin Fitting:
*Set Theory and the Continuum Problem*(revised ed.) ... (previous) ... (next): Chapter $1$: General Background: $\S 6$ Significance of the results - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**axiomatic set theory**