Coloring finite subsets of uncountable sets
Abstract
It is consistent for every (1 <= n< omega) that (2^omega = omega_n) and there is a function (F:[omega_n]^{< omega}> omega) such that every finite set can be written at most (2^n1) 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 1995
 arXiv:
 arXiv:math/9505216
 Bibcode:
 1995math......5216K
 Keywords:

 Mathematics  Logic
 EPrint:
 Proc. Amer. Math. Soc. 124 (1996), 35013505