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A partition theorem for pairs of finite sets

Thomas Jech·Saharon Shelah
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Abstract

Every partition of [[omega_1]^{< omega}]^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.

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Thomas Jech, Saharon Shelah. 1991-01-15. A partition theorem for pairs of finite sets. https://arxiv.org/abs/math/9201248

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