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A partition theorem for pairs of finite sets


Authors: Thomas Jech and Saharon Shelah
Journal: J. Amer. Math. Soc. 4 (1991), 647-656
MSC: Primary 03E05; Secondary 03E35, 04A20, 05D10
DOI: https://doi.org/10.1090/S0894-0347-1991-1122043-8
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 [Enhancements On Off] (What's this?)

  • [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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Additional Information

DOI: https://doi.org/10.1090/S0894-0347-1991-1122043-8
Article copyright: © Copyright 1991 American Mathematical Society

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