Infinite monochromatic sumsets for colourings of the reals

by Komjath and Leader and Russell and Shelah and Soukup and Vidnyanszky. [KLRSSV:1129]

N. Hindman, I. Leader and D. Strauss proved that it is consistent that there is a finite coloring of {R} so that no infinite sumset X + X is monochromatic. The (rather fascinating) question if the same conclusion holds in ZFC was open until now: we show that under certain set theoretic assumptions for any c: {R}-> r with r finite there is an infinite X subseteq {R} so that C upharpoonright X + X is constant.

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