arXiv:2203.06156 Abstract | arXiv Analytics

arXiv:2203.06156 [math.LO]Abstract References Reviews Resources

Hindman's Theorem in the hierarchy of Choice Principles

Published 2022-03-11Version 1

In the context of $\mathsf{ZF}$, we analyze a version of Hindman's finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the $\mathsf{AC}$.

Comments: 17 pages, 2 figures

Categories: math.LO

Subjects: 03E25, 03E35, 03E30, 03E65, 03E02, 03E05

Keywords: hindmans theorem, hindmans finite unions theorem, classical weak choice principles, weak form, infinite sets

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