Bulletin of Symbolic Logic 25 (2):208-212 (2019)

Authors
Jouko A Vaananen
University of Helsinki
Abstract
We show that if $$ satisfies the first-order Zermelo–Fraenkel axioms of set theory when the membership relation is ${ \in _1}$ and also when the membership relation is ${ \in _2}$, and in both cases the formulas are allowed to contain both ${ \in _1}$ and ${ \in _2}$, then $\left \cong \left$, and the isomorphism is definable in $$. This extends Zermelo’s 1930 theorem in [6].
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DOI 10.1017/bsl.2019.15
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