# Sh:516

• Komjáth, P., & Shelah, S. (1996). Coloring finite subsets of uncountable sets. Proc. Amer. Math. Soc., 124(11), 3501–3505.
• Abstract:
It is consistent for every 1\leq n< \omega that 2^\omega=\omega_n and there is a function F:[\omega_n]^{< \omega}\to\omega such that every finite set can be written at most 2^n-1 ways as the union of two distinct monocolored sets. If GCH holds, for every such coloring there is a finite set that can be written at least \sum^n_{i=1}{n+i\choose n}{n\choose i} ways as the union of two sets with the same color.
• published version (5p)
Bib entry
@article{Sh:516,
author = {Komj{\'a}th, P{\'e}ter and Shelah, Saharon},
title = {{Coloring finite subsets of uncountable sets}},
journal = {Proc. Amer. Math. Soc.},
fjournal = {Proceedings of the American Mathematical Society},
volume = {124},
number = {11},
year = {1996},
pages = {3501--3505},
issn = {0002-9939},
mrnumber = {1342032},
mrclass = {03E05 (03E35)},
doi = {10.1090/S0002-9939-96-03450-8},
note = {\href{https://arxiv.org/abs/math/9505216}{arXiv: math/9505216}},
arxiv_number = {math/9505216}
}