Pairwise Sums in the Reals

Pairwise Sums in the Reals

Update: 2015-12-23
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Co-authors: Neil Hindman (Howard University), Dona Strauss (University of Leeds)

We show (assuming CH) that there is a finite colouring of the reals such that no infinite set X has X+X (meaning the pairwise sums from X, allowing repetition) monochromatic. And we give positive results for ‘nice’ colourings.
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Pairwise Sums in the Reals

Pairwise Sums in the Reals

Vincenzo Abete