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- W4300636830 abstract "We show, in Zermelo-Fraenkel set theory without the Axiom of Choice, that the existence of a discontinuous homomorphism of the additive group of real numbers induces a selector for the Vitali equivalence relation $mathbb{R}/mathbb{Q}$. This shows that a nonprincipal ultrafilter on the integers is not sufficient to construct a discontinuous automorphism of the complex field, confirming a conjecture of Simon Thomas. This is an improved version of our paper in the Proceedings of the American Mathematical Society, which used a weak version of the Axiom of Choice for the same result." @default.
- W4300636830 created "2022-10-03" @default.
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- W4300636830 date "2018-03-07" @default.
- W4300636830 modified "2023-10-18" @default.
- W4300636830 title "Discontinuous homomorphisms, selectors and automorphisms of the complex field" @default.
- W4300636830 doi "https://doi.org/10.48550/arxiv.1803.02740" @default.
- W4300636830 hasPublicationYear "2018" @default.
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