The Erdos-Moser sum-free set problem

TL;DR

This paper proves that any finite set of integers contains a relatively large subset where the sum of any two distinct elements is not in the original set, advancing understanding of sum-free subsets.

Contribution

It establishes the existence of large sum-free subsets of a specific size in any finite integer set, addressing the Erdos-Moser problem.

Findings

Existence of sum-free subsets of size rac{ |A|^{1+c}} in any finite integer set

Subsets are of size logarithmic to the original set with an exponent greater than 1

Provides bounds on the size of sum-free subsets in finite sets

Abstract

We show that if A is a finite set of integers then it has a subset S of size \log^{1+c} |A| (c>0 absolute) such that s+s' is never in A when s and s' are distinct elements of S.