# Sh:516

- Komjáth, P., & Shelah, S. (1996).
*Coloring finite subsets of uncountable sets*. Proc. Amer. Math. Soc.,**124**(11), 3501–3505. arXiv: math/9505216 DOI: 10.1090/S0002-9939-96-03450-8 MR: 1342032 -
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}, doi = {10.1090/S0002-9939-96-03450-8}, mrclass = {03E05 (03E35)}, mrnumber = {1342032}, mrreviewer = {Marion Scheepers}, doi = {10.1090/S0002-9939-96-03450-8}, note = {\href{https://arxiv.org/abs/math/9505216}{arXiv: math/9505216}}, arxiv_number = {math/9505216} }