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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


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

© 1996-9 Eric W. Weisstein