An extension of a theorem of Zermelo
Logic
2019-07-31 v1
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.
Keywords
Cite
@article{arxiv.1808.08621,
title = {An extension of a theorem of Zermelo},
author = {Jouko Väänänen},
journal= {arXiv preprint arXiv:1808.08621},
year = {2019}
}