Claims

../

1971_12_01_choi: Choi's 1971 bound g(n) << n^{2/5+o(1)} (Proc. London Math. Soc.), the first power-saving upper bound for the Erdős–Moser function, with the reduction to integer sets; refereed, known here through the papers that cite it.

2005_03_01_ruzsa: The Theorem of Ruzsa (Ramanujan J. 2005): some n positive integers have no sum-avoiding subset larger than a constant times exp(c sqrt(log n)), for every c > sqrt(8 log 2); the best upper bound for g(n); refereed.

2018_04_10_sanders: Theorem 1.2 of Sanders (Canad. J. Math. 2021): every finite set A of integers has a subset of size at least (log |A|)^{1+c}, c > 0 absolute, with no sum of two distinct elements in A; refereed.

2025_01_17_beker: Theorem 1.2 of Beker's preprint (accepted by Int. Math. Res. Not.): for every c < 1/68, every large finite set A of integers has a subset of size at least (log |A|)^{1+c} with no sum of two distinct elements in A; no journal record on 2026-10-07.

---