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arXiv · 1703.06706

A note on Hindman-type theorems for uncountable cardinals

Lorenzo Carlucci
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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.

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Lorenzo Carlucci. 2017-03-20. A note on Hindman-type theorems for uncountable cardinals. https://arxiv.org/abs/1703.06706

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