Real Analysis Exchange

A Certain 2-Coloring of the Reals

Péter Komjáth

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Article information

Source
Real Anal. Exchange, Volume 41, Number 1 (2016), 227-232.

Dates
First available in Project Euclid: 29 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.rae/1490752824

Mathematical Reviews number (MathSciNet)
MR3511943

Zentralblatt MATH identifier
1381.03036

Subjects
Primary: 05D10: Ramsey theory [See also 05C55] 03E05: Other combinatorial set theory

Keywords
Ramsey theory coloring the reals Sierpinski’s theorem

Citation

Komjáth, Péter. A Certain 2-Coloring of the Reals. Real Anal. Exchange 41 (2016), no. 1, 227--232. https://projecteuclid.org/euclid.rae/1490752824


Export citation