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arXiv · 1710.07500

Infinite monochromatic sumsets for colourings of the reals

Péter Komjáth·Imre Leader·Paul A. Russell·Saharon Shelah·Dániel T. Soukup·Zoltán Vidnyánszky
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Abstract

N. Hindman, I. Leader and D. Strauss proved that it is consistent that there is a finite colouring of $\mathbb R$ so that no infinite sumset $X+X=\{x+y:x,y\in X\}$ is monochromatic. Our aim in this paper is to prove a consistency result in the opposite direction: we show that, under certain set-theoretic assumptions, for any $c:\mathbb R\to r$ with $r$ finite there is an infinite $X\subseteq \mathbb R$ so that $c$ is constant on $X+X$.

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Péter Komjáth, Imre Leader, Paul A. Russell, Saharon Shelah, Dániel T. Soukup, Zoltán Vidnyánszky. 2017-10-20. Infinite monochromatic sumsets for colourings of the reals. https://arxiv.org/abs/1710.07500

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