Coloring finite subsets of uncountable sets

Details Coloring finite subsets of uncountable sets Coloring finite subsets of uncountable sets

1995-05-15

arxiv.org/abs/math/9505216v1

Proc. Amer. Math. Soc. 124 (1996), 3501-3505

Mathematics

Logic

Scientific paper

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^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.

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