The Erdős–Moser Sum-free Set Problem

Source abstract

Abstract 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 $3$ .)