A partition theorem for pairs of finite sets
Thomas Jech and Saharon Shelah
J. Amer. Math. Soc. 4 (1991), 647-656
Primary 03E05; Secondary 03E35, 04A20, 05D10
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Abstract: Every partition of 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.
F. Galvin, seminar notes from U.C.L.A.
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- R. Graham, B. Rothschild, and J. Spencer, Ramsey Theory, Wiley, New York, 1980. MR 591457 (82b:05001)
- T. Jech, Some combinatorial problems concerning uncountable cardinals, Ann. Math. Logic 5 (1973), 165-198. MR 0325397 (48:3744)
- R. Laver, private communication.
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