Discontinuous homomorphisms, selectors and automorphisms of the complex field. (arXiv:1803.02740v1 [math.LO])

We show, assuming a weak form of 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. 查看全文>>