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
MathSciNet review: 1122043
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.
-  Ronald L. Graham, Bruce L. Rothschild, and Joel H. Spencer, Ramsey theory, John Wiley & Sons, Inc., New York, 1980. Wiley-Interscience Series in Discrete Mathematics; A Wiley-Interscience Publication. MR 591457
-  Thomas J. Jech, Some combinatorial problems concerning uncountable cardinals, Ann. Math. Logic 5 (1972/73), 165–198. MR 0325397, https://doi.org/10.1016/0003-4843(73)90014-4
-  R. Laver, private communication.
- F. Galvin, seminar notes from U.C.L.A.
- 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.