A note on Hindman-type theorems for uncountable cardinals
Combinatorics
2025-06-12 v1 Logic
Abstract
Recent results of Hindman, Leader and Strauss and of Fern\'andez-Bret\'on and Rinot showed that natural versions of Hindman's Theorem fail {\em for all} uncontable cardinals. On the other hand, Komj\'ath proved a result in the positive direction, showing that {\em there are} arbitrarily large abelian groups satisfying {\em some} Hindman-type property. In this note we show how a family of natural Hindman-type theorems for uncountable cardinals can be obtained by adapting some recent results of the author from their original countable setting. We also show how lower bounds for {\em some} of the variants considered can be obtained.
Keywords
Cite
@article{arxiv.1703.06706,
title = {A note on Hindman-type theorems for uncountable cardinals},
author = {Lorenzo Carlucci},
journal= {arXiv preprint arXiv:1703.06706},
year = {2025}
}