Open Access
2016 A Certain 2-Coloring of the Reals
Péter Komjáth
Real Anal. Exchange 41(1): 227-232 (2016).


There is a function $F:[\mathfrak{c}]^{\lt\omega}\to\{0,1\}$ such that if $A\subseteq [\mathfrak{c}]^{\lt\omega}$ is uncountable, then $\{F(a\cup b):a,b\in A, a\neq b\}=\{0,1\}$. A corollary is that there is a function $f:\mathbb{R}\to\{0,1\}$ such that if $A\subseteq\mathbb{R}$ is uncountable, $2\leq k\lt\omega$, then both 0 and 1 occur as the value of $f$ at the sum of $k$ distinct elements of $A$. This was originally proved by Hindman, Leader, and Strauss under CH, and they asked if it holds in general.


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Péter Komjáth. "A Certain 2-Coloring of the Reals." Real Anal. Exchange 41 (1) 227 - 232, 2016.


Published: 2016
First available in Project Euclid: 29 March 2017

zbMATH: 1381.03036
MathSciNet: MR3511943

Primary: 03E05 , 05D10

Keywords: coloring the reals , Ramsey theory , Sierpinski’s theorem

Rights: Copyright © 2016 Michigan State University Press

Vol.41 • No. 1 • 2016
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