A polarized partition relation for cardinals of countable cofinality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

A polarized partition relation for cardinals of countable cofinality

Authors:	Albin L. Jones

Affiliation:	2153 Oakdale Rd., Pasadena, Maryland 21122

Abstract:	We prove that if and $lambda = 2^{<kappa}$ , then $displaystyle left( begin{matrix} lambda^+ lambda end{matrix}right) t... ...egin{matrix} lambda^+ & alpha lambda & kappa end{matrix}right)^{1,1}$ for all . This polarized partition relation holds if for every partition either there are $B_0 in [lambda]^{lambda}$ and $A_0 in [lambda^+]^{lambda^+}$ with or there are $B_1 in [kappa]^{lambda}$ and $A_1 in [alpha]^{lambda^+}$ with .

Keywords:	Transfinite cardinal countable cofinality elementary substructure transfinite ordinal polarized partition relation Ramsey theory regular cardinal singular cardinal

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