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Preprint Number 1327

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1327. Péter Komjáth, Imre Leader, Paul A. Russell, Saharon Shelah, Dániel T. Soukup, Zoltán Vidnyánszky
Infinite monochromatic sumsets for colourings of the reals
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Submission date: 20 October 2017

Abstract:

N. Hindman, I. Leader and D. Strauss proved that it is consistent that there is a finite colouring of 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:R --> r with r finite there is an infinite X ⊆ R so that c is constant on X+X.

Mathematics Subject Classification: 03E02, 03E35, 05D10

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Full text arXiv 1710.07500: pdf, ps.


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