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The Erdős–Moser Sum-free Set Problem
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 73 / Issue 1 / February 2021
- Published online by Cambridge University Press:
- 23 September 2019, pp. 63-107
- Print publication:
- February 2021
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- Article
- Export citation
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We show that there is an absolute
$c>0$ such that if 
$A$ is a finite set of integers, then there is a set 
$S\subset A$ of size at least 
$\log ^{1+c}|A|$ such that the restricted sumset 
$\{s+s^{\prime }:s,s^{\prime }\in S\text{ and }s\neq s^{\prime }\}$ is disjoint from 
$A$. (The logarithm here is to base 
$3$.)
