# On a question of Erdős and Moser

```@article{Sudakov2005OnAQ,
title={On a question of Erdős and Moser},
author={Benny Sudakov and Endre Szemer{\'e}di and Van H. Vu},
journal={Duke Mathematical Journal},
year={2005},
volume={129},
pages={129-155}
}```
• Published 15 July 2005
• Mathematics
• Duke Mathematical Journal
For two finite sets of real numbers A and B, one says that B is sum-free with respect to A if the sum set {b + b | b, b ∈ B, b 6= b} is disjoint from A. Forty years ago, Erdős and Moser posed the following question. Let A be a set of n real numbers. What is the size of the largest subset B of A which is sum-free with respect to A? In this paper, we show that any set A of n real numbers contains a set B of cardinality at least g(n) ln n which is sum-free with respect to A, where g(n) tends to…

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