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Hindman’s Theorem is only a Countable Phenomenon

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Abstract

We pursue the idea of generalizing Hindman’s Theorem to uncountable cardinalities, by analogy with the way in which Ramsey’s Theorem can be generalized to weakly compact cardinals. But unlike Ramsey’s Theorem, the outcome of this paper is that the natural generalizations of Hindman’s Theorem proposed here tend to fail at all uncountable cardinals.

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Correspondence to David J. Fernández-Bretón.

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The author was partially supported by postdoctoral fellowship number 263820 from the Consejo Nacional de Ciencia y Tecnología (Conacyt), Mexico.

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Fernández-Bretón, D.J. Hindman’s Theorem is only a Countable Phenomenon. Order 35, 83–91 (2018). https://doi.org/10.1007/s11083-016-9419-7

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  • DOI: https://doi.org/10.1007/s11083-016-9419-7

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