Zermelo Set Theory

The version of set theory obtained if Axiom 6 of Zermelo-Fraenkel Set Theory is replaced by

6'. Axiom of subsets: for any set-theoretic formula $A(u)$, $\forall x\exists y\forall u(u\in y\rightleftharpoons u\in x \wedge A(u))$,

which can be deduced from Axiom 6.

See also Zermelo-Fraenkel Set Theory

References

Iyanaga, S. and Kawada, Y. (Eds.). ``Zermelo-Fraenkel Set Theory.'' §35B in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 135, 1980.