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Hindman’s theorem in the hierarchy of choice principles
Journal of Mathematical Logic 24 (1) (2023)
Abstract
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].Author's Profile
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References found in this work
Zermelo-Fraenkel consistency results by Fraenkel-Mostowski methods.David Pincus - 1972 - Journal of Symbolic Logic 37 (4):721-743.
On ramsey’s theorem and the existence of infinite chains or infinite anti-chains in infinite posets.Eleftherios Tachtsis - 2016 - Journal of Symbolic Logic 81 (1):384-394.
Ramsey's theorem in the hierarchy of choice principles.Andreas Blass - 1977 - Journal of Symbolic Logic 42 (3):387-390.
Some Aspects and Examples of Infinity Notions.J. W. Degen - 1994 - Mathematical Logic Quarterly 40 (1):111-124.
Ramsey’s theorem and König’s Lemma.T. E. Forster & J. K. Truss - 2007 - Archive for Mathematical Logic 46 (1):37-42.
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