The version of set theory obtained if Axiom 6 of Zermelo-Fraenkel set theory is replaced by 6'. Selection axiom (or "axiom of subsets"): for any set-theoretic formula A(u), for all x exists y for all u(u element y congruent u element x⋀A(u)), which can be deduced from Axiom 6. However, there seems to be some disagreement in the literature about just which axioms of Zermelo-Fraenkel set theory constitute "Zermelo Set Theory." Mendelson does not include the axioms of choice, foundation, replacement In Zermelo set theory, but does includes 6'. However, Enderton includes the axioms of choice and foundation, but does not include the axioms of replacement or Selection.

set theory | Zermelo-Fraenkel set theory

Ernst Friedrich Ferdinand Zermelo