Ricerc@Sapienza

Recent results of Hindman, Leader and Strauss and of Fernández-Bretón and Rinot showed that natural versions of Hindman’s Theorem fail for all uncontable cardinals. On the other hand, Komjáth proved a result in the positive direction, showing that there are arbitrarily large abelian groups satisfying 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.