Baire sets of $k$-parameter words are Ramsey
HTML articles powered by AMS MathViewer
- by Hans Jürgen Prömel and Bernd Voigt PDF
- Trans. Amer. Math. Soc. 291 (1985), 189-201 Request permission
Abstract:
We show that Baire sets of $k$-parameter words are Ramsey. This extends a result of Carlson and Simpson, A dual form of Ramsey’s theorem, Adv. in Math. 53 (1984), 265-290. Employing the method established therefore, we derive analogous results for Dowling lattices and for ascending $k$-parameter words.References
-
T. Carlson, in preparation, cf. [CS84].
- Timothy J. Carlson and Stephen G. Simpson, A dual form of Ramsey’s theorem, Adv. in Math. 53 (1984), no. 3, 265–290. MR 753869, DOI 10.1016/0001-8708(84)90026-4
- W. Deuber and B. Voigt, Partitionseigenschaften endlicher affiner und projektiver Räume, European J. Combin. 3 (1982), no. 4, 329–340 (German, with English summary). MR 687731, DOI 10.1016/S0195-6698(82)80017-6
- T. A. Dowling, A class of geometric lattices based on finite groups, J. Combinatorial Theory Ser. B 14 (1973), 61–86. MR 307951, DOI 10.1016/s0095-8956(73)80007-3
- Adam Emeryk, Ryszard Frankiewicz, and Włdysław Kulpa, On functions having the Baire property, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), no. 6, 489–491 (English, with Russian summary). MR 560185
- R. L. Graham and B. L. Rothschild, Ramsey’s theorem for $n$-parameter sets, Trans. Amer. Math. Soc. 159 (1971), 257–292. MR 284352, DOI 10.1090/S0002-9947-1971-0284352-8
- A. W. Hales and R. I. Jewett, Regularity and positional games, Trans. Amer. Math. Soc. 106 (1963), 222–229. MR 143712, DOI 10.1090/S0002-9947-1963-0143712-1
- Neil Hindman, Finite sums from sequences within cells of a partition of $N$, J. Combinatorial Theory Ser. A 17 (1974), 1–11. MR 349574, DOI 10.1016/0097-3165(74)90023-5
- K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751 K. Leeb, Vorlesungen über Pascaltheorie, Erlangen, 1973.
- Keith R. Milliken, Ramsey’s theorem with sums or unions, J. Combinatorial Theory Ser. A 18 (1975), 276–290. MR 373906, DOI 10.1016/0097-3165(75)90039-4
- C. St. J. A. Nash-Williams, On well-quasi-ordering transfinite sequences, Proc. Cambridge Philos. Soc. 61 (1965), 33–39. MR 173640, DOI 10.1017/s0305004100038603 K. Prikry, In these notes I give..., handwritten manuscript, November 1982. H. J. Prömel, S. G. Simpson and B. Voigt, A dual form of Erdös-Rado’s canonization theorem, J. Combin. Theory Ser. A (to appear).
- Alan D. Taylor, A canonical partition relation for finite subsets of $\omega$, J. Combinatorial Theory Ser. A 21 (1976), no. 2, 137–146. MR 424571, DOI 10.1016/0097-3165(76)90058-3
- Bernd Voigt, The partition problem for finite abelian groups, J. Combin. Theory Ser. A 28 (1980), no. 3, 257–271. MR 570208, DOI 10.1016/0097-3165(80)90069-2 —, Parameter words, trees and vector spaces, preprint, Bielefeld, 1983.
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 291 (1985), 189-201
- MSC: Primary 05A17; Secondary 04A20
- DOI: https://doi.org/10.1090/S0002-9947-1985-0797054-6
- MathSciNet review: 797054