Zermelo–Fraenkel set theory
STANDARD FORM OF AXIOMATIC SET THEORY
Zermelo-Fraenkel axiom; ZFC; Zermelo-Fraenkel axioms; Zermelo-Frankel axioms; Zermelo-Frankel set theory; ZFC set theory; Zermelo-Fraenkel framework; ZFC Set Theory; Zermelo-Fränkel set theory; Zermelo-Frankel; Zfc; ZFC set; ZF axioms; Zermelo–Frankel set theory; Zermelo-Fraenkel set theory; ZF set theory; Zermelo-Fraenkel-Skolem set theory; Zermelo-Frankel axiom; Zermelo–Fraenkel axioms; Zermelo Fraenkel set theory; Zermelo-Fraenkel; Zermelo–Fraenkel axiomatization; Zermelo-Fraenkel axiomatization; Zermelo-Fränkel; ZFC Set theory; Zermelo–Fraenkel axiom; Zermelo–Fraenkel framework; Zermelo–Fraenkel; Zermelo-frankel; Zermelo–Fraenkel set theory with the axiom of choice; Axioms of ZF; Zermelo−Fraenkel set theory; Zermelo-Fraenkel set theory with the axiom of choice
In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.