Definition:Axiomatic Set Theory

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)

ZFC (Zermelo-Fraenkel with the Axiom of Choice).

Lesser known examples include:

Von Neumann-Bernays-Gödel Set Theory

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
• 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Introduction
• 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): axiomatic set theory