Coloring finite subsets of uncountable sets

Péter Komjáth; Saharon Shelah

doi:10.1090/s0002-9939-96-03450-8

Coloring finite subsets of uncountable sets

Péter Komjáth^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

It is consistent for every 1 ≤ n < ω that 2^ω = ω_n and there is a function F : [ω_n]^<ω → ω such that every finite set can be written in at most 2ⁿ-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 1/2 ∑_i=1ⁿ (_nⁿ⁺ⁱ) (_iⁿ) ways as the union of two sets with the same color.

Original language	English
Pages (from-to)	3501-3505
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	124
Issue number	11
DOIs	https://doi.org/10.1090/s0002-9939-96-03450-8
State	Published - 1996

Keywords

Axiomatic set theory
Combinatorial set theory
Independence proofs

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Coloring finite subsets of uncountable sets

Abstract

Keywords

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