Hindman's Theorem is only a countable phenomenon
arXiv:1506.05834 · doi:10.1007/s11083-016-9419-7
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.
11 pages, some minor referee-suggested revisions performed