Coloring finite subsets of uncountable sets期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Coloring finite subsets of uncountable sets

Authors:	Pé ter Komjá th Saharon Shelah

Affiliation:	Department of Computer Science, Eötvös University, Budapest, Múzeum krt.~6--8, 1088, Hungary ; Institute of Mathematics, Hebrew University, Givat Ram, 91904, Jerusalem, Israel

Abstract:	It is consistent for every that $2^{omega }=omega _{n}$ and there is a function $F:[omega _{n}]^{< omega }to omega$ such that every finite set can be written in 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 $frac {1}{2}sum ^{n}_{i=1}{binom {n+i}{n}}{binom {n}{i}}$ ways as the union of two sets with the same color.

Keywords:	Axiomatic set theory independence proofs combinatorial set theory

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载全文