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