Hindman’s Theorem is only a Countable Phenomenon

David J. Fernández-Bretón

doi:10.1007/s11083-016-9419-7

Hindman’s Theorem is only a Countable Phenomenon

David J. Fernández-Bretón

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English
Pages (from-to)	83-91
Number of pages	9
Journal	Order
Volume	35
Issue number	1
DOIs	https://doi.org/10.1007/s11083-016-9419-7
State	Published - 1 Mar 2018
Externally published	Yes

Keywords

Abelian groups
Hindman’s theorem
Ramsey-type theorem
Semigroups
Uncountable cardinals
Δ-system lemma

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10.1007/s11083-016-9419-7

Cite this

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KW - Ramsey-type theorem

KW - Semigroups

KW - Uncountable cardinals

KW - Δ-system lemma

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Hindman’s Theorem is only a Countable Phenomenon

Abstract

Keywords

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