Abstract
Generalizing earlier results of Moran and Strauss (Mathematika 27, 1980, 213–244) and of Carlson and Simpson (Adv. in Math. 53, 1984, 265–290) it was shown in Prömel and Voigts (Trans. Amer. Math. Soc. 291, 1985, 198–201) that Baire sets ofk-parameter words are Ramsey. Motivated by the “duality” between category and measure, we investigate in this paper measurable sets ofk parameter words. We show that measurable sets of ascendingk-parameter words are Ramsey, whereas in general measurable sets ofk-parameter words fail to be Ramsey.
Similar content being viewed by others
References
T. J. Carlson: Some unifying principles in Ramsey Theory,Discrete Math. 68, 1988, 117–168.
T. J. Carlson, andS. G. Simpson: A dual form of Ramsey's theorem,Adv. in Math. 53, 1984, 265–290.
R. L. Graham, andB. L. Rothschild: Ramsey's theorem forn-parameter sets,Trans. Amer. Math. Soc. 159, 1971, 257–292.
R. L. Graham, B. L. Rothschild, andJ. H. Spencer: Ramsey's Theory, John Wiley, New York, 1980.
A. W. Hales, andR. I. Jewett: Regularity and positional games,Trans. Amer. Math. Soc.,106, 1963, 222–229.
N. Hindman: Finite sums from sequences within cells of a partion of ℕ,J. Combin. Theory Ser. A.17, 1974, 1–11.
K. Kuratowski: Topology Vol I, Academic Press, New York, 1966.
K. Milliken: Ramsey's theorem with sums or unions,J. Combin. Theory Ser. A.18, 1975, 276–190.
G. Moran, andD. Strauss: Countable partitions of product spaces,Mathematika 27, 1980, 213–224.
H. J. Prömel, andB. Voigt: Baire sets ofk-parameter words are Ramsey,Trans. Amer. Math. Soc. 291, 1985, 189–201.
H. J. Prömel, andB. Voigt: Graham Rothschild parameter sets, in: The Mathematics of Ramsey Theory (J. Nešetřil and V. Rödl, eds.), Springer-Verlag, Berlin, 1990, 113–149.
H. J. Prömel, andB. Voigt: Aspects of Ramsey Theory, in preparation.
S. Shelah: Can you take Solovay's inaccessible away?,Israel J. of Math. 48, 1984, 1–47.
B. Voigt: Ellentuck type theorems, to appear inThe Journal of Symbolic Logic.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Prömel, H.J., Voigt, B. Graham-Rothschild parameter words and measurable partitions. Combinatorica 11, 253–259 (1991). https://doi.org/10.1007/BF01205077
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01205077