Strong partition properties for infinite cardinals
Strong partition properties for infinite cardinals
复制标题
无限基数的强划分性质
DOI：
10.2307/2270698
复制
发表时间：
1970
影响因子：
0.6
通讯作者：
E. Kleinberg
中科院分区：
文献类型：
--
作者：
E. Kleinberg
过去几年在集合论的背景下研究的“划分关系”的概念，是由F.P.Ramsey[14]的下列定理启发的：定理0.1。设n是正整数，{A，B}是恰好包含n个元素的非负整数的子集的划分。则存在一个非负整数的无限子集x，其所有n元子集只包含在A或B中的一个中(任何这样的集合x都被称为对该划分是“齐次的”)。
The notion of a “partition relation”, as it has been studied in the context of set theory for the past several years, was inspired by the following theorem of F. P. Ramsey [14]: Theorem 0.1. Let n be a positive integer and let {A, B} be a partition of those subsets of the nonnegative integers containing exactly n elements. Then there exists an infinite subset x of the nonnegative integers all of whose n-element subsets are contained in only one of A or B. (Any such set x is said to be “homogeneous” for the partition.)