Journal of the American Mathematical Society

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ISSN 1088-6834(e) ISSN 0894-0347(p)

A partition theorem for pairs of finite sets

Author(s): Thomas Jech; Saharon Shelah
Journal: J. Amer. Math. Soc. 4 (1991), 647-656.
MSC: Primary 03E05; Secondary 03E35, 04A20, 05D10
MathSciNet review: 1122043
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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.

References:

[1]: F. Galvin, seminar notes from U.C.L.A.
[2]: R. Graham, B. Rothschild, and J. Spencer, Ramsey Theory, Wiley, New York, 1980. MR 591457 (82b:05001)
[3]: T. Jech, Some combinatorial problems concerning uncountable cardinals, Ann. Math. Logic 5 (1973), 165-198. MR 0325397 (48:3744)
[4]: R. Laver, private communication.

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