Title: Infinite monochromatic sumsets for colourings of the reals,
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 $X+X$.