2017/10/20 by Komjáth, Péter, Leader, Imre, Russell, Paul A. +3
#03E02 #03E35 #05D10 #Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1710.07500
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∈ 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→ r with r finite there is an infinite X⊆ \mathbb R so that c is constant on X+X.