A partition theorem for pairs of finite sets
HTML articles powered by AMS MathViewer
- by Thomas Jech and Saharon Shelah
- J. Amer. Math. Soc. 4 (1991), 647-656
- DOI: https://doi.org/10.1090/S0894-0347-1991-1122043-8
- PDF | Request permission
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
- F. Galvin, seminar notes from U.C.L.A.
- Ronald L. Graham, Bruce L. Rothschild, and Joel H. Spencer, Ramsey theory, Wiley-Interscience Series in Discrete Mathematics, John Wiley & Sons, Inc., New York, 1980. MR 591457
- Thomas J. Jech, Some combinatorial problems concerning uncountable cardinals, Ann. Math. Logic 5 (1972/73), 165–198. MR 325397, DOI 10.1016/0003-4843(73)90014-4 R. Laver, private communication.
Bibliographic Information
- © Copyright 1991 American Mathematical Society
- 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