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arXiv · 1808.08621

An extension of a theorem of Zermelo

Jouko Väänänen
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Abstract

We show that if (M,E,E') satisfies the first order Zermelo-Fraenkel axioms of set theory when the membership relation is E and also when the membership relation is E', and in both cases the formulas are allowed to contain both E and E', then (M,E) and (M,E') are isomorphic, and the isomorphism is definable in (M,E,E'). This extends Zermelo's 1930 theorem about second order ZFC.

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Jouko Väänänen. 2018-08-26. An extension of a theorem of Zermelo. https://doi.org/10.1017/bsl.2019.15

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