Partition theorem for pairs of finite sets

Thomas Jech; Saharon Shelah

doi:10.1090/S0894-0347-1991-1122043-8

Partition theorem for pairs of finite sets

Thomas Jech
, Saharon Shelah

Einstein Institute of Mathematics

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

6 Scopus citations

Abstract

Every partition of [[ω₁]^<ω]² into finitely many pieces has a cofinal homogeneous set. Furthermore, it is consistent that every directed partially ordered set satisfies the partition property if and only if it has finite character.

Original language	English
Pages (from-to)	647-656
Number of pages	10
Journal	Journal of the American Mathematical Society
Volume	4
Issue number	4
DOIs	https://doi.org/10.1090/S0894-0347-1991-1122043-8
State	Published - Oct 1991

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title = "Partition theorem for pairs of finite sets",

abstract = "Every partition of [[ω1]<ω]2 into finitely many pieces has a cofinal homogeneous set. Furthermore, it is consistent that every directed partially ordered set satisfies the partition property if and only if it has finite character.",

author = "Thomas Jech and Saharon Shelah",

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Partition theorem for pairs of finite sets

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