Hindman's Theorem is only a countable phenomenon
Combinatorics
2018-03-16 v3 Logic
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.
Keywords
Cite
@article{arxiv.1506.05834,
title = {Hindman's Theorem is only a countable phenomenon},
author = {David J. Fernández-Bretón},
journal= {arXiv preprint arXiv:1506.05834},
year = {2018}
}
Comments
11 pages, some minor referee-suggested revisions performed