Hindman’s theorem in the hierarchy of choice principles. (English) Zbl 07797270
Summary: 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 \(\mathsf{AC}\).
MSC:
| 03E25 | Axiom of choice and related propositions |
| 03E35 | Consistency and independence results |
| 03E30 | Axiomatics of classical set theory and its fragments |
| 03E65 | Other set-theoretic hypotheses and axioms |
| 03E02 | Partition relations |
| 03E05 | Other combinatorial set theory |
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