Hindman’s theorem in the hierarchy of choice principles
David J. Fernández-Bretón · Journal of Mathematical Logic · 2023
In the context of [Formula: see text], 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 [Formula: see text].