Ultrafilters and ramsey theory — An update

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Part of the Lecture Notes in Mathematics book series (LNM, volume 1401)


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  1. 1.
    R. Arens, The adjoint of a bilinear operator, Proc. Amer. Math. Soc. 2 (1951), 839–848.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    V. Bergelson, A density statement generalizing Schur’s Theorem, J. Comb. Theory (Series A) 43 (1986), 338–343.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    V. Bergelson, Ergodic Ramsey Theory, in Logic and Combinatorics ed., S. Simpson, Contemporary Mathematics 69 (1987), 63–87.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    V. Bergelson and N. Hindman, A combinatorially large cell of a partition of N, J. Comb. Theory (Series A), to appear.Google Scholar
  5. 5.
    V. Bergelson and N. Hindman, Density versions of two generalizations of Schur’s Theorem, J. Comb. Theory (Series A), to appear.Google Scholar
  6. 6.
    V. Bergelson and N. Hindman, Ultrafilters and multidimensional Ramsey theorems, manuscript.Google Scholar
  7. 7.
    V. Bergelson and B. Weiss, Translation properties of sets of positive upper density, Proc. Amer. Math. Soc. 94 (1985), 371–376.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    J. Berglund and N. Hindman, Filters and the weak almost periodic compactification of a discrete semigroup, Trans. Amer. Math. Soc. 284 (1984), 1–38.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    J. Berglund, H. Junghenn, and P. Milnes, Compact right topological semigroups and generalizations of almost periodicity, Lecture Notes in Math. 663, Springer-Verlag, Berlin (1978).zbMATHGoogle Scholar
  10. 10.
    A. Blass, Selective ultrafilters and homogeneity, Annals of Pure and Applied Logic, to appear.Google Scholar
  11. 11.
    A. Blass, Ultrafilters related to Hindman’s finite-unions theorem and its extensions, in Logic and Combinatorics, ed. S. Simpson, Contemporary Mathematics 65 (1987), 89–124.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    A. Blass and N. Hindman, On strongly summable ultrafilters and union ultrafilters, Trans. Amer. Math. Soc., 304, (1987), 93–99.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    T. Carlson, Some unifying principles in Ramsey Theory, Discrete Math., to appear.Google Scholar
  14. 14.
    W. Comfort, Some recent applications of ultrafilters to topology, in Proceedings of the Fourth Prague topological Symposium, 1976, ed. J. Novak, Lecture Notes in Math. 609 (1977), 34–42.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    W. Comfort, Ultrafilters: an interim report, Surveys in General Topology, Academic Press, New York, 1980, 33–54.Google Scholar
  16. 16.
    W. Comfort and S. Negrepontis, The theory of ultrafilters, Springer-Verlag, Berlin, 1974.CrossRefzbMATHGoogle Scholar
  17. 17.
    D. Davenport, The algebraic properties of closed subsemigroups of ultrafilters on a discrete semigroup, Dissertation, Howard University, 1987.Google Scholar
  18. 18.
    D. Davenport and N. Hindman, Subprincipal closed ideals in βN, Semigroup Forum, to appear.Google Scholar
  19. 19.
    M. Day, Amenable semigroups, Illinois J. Math. 1 (1957), 509–544.MathSciNetzbMATHGoogle Scholar
  20. 20.
    W. Deuber and N. Hindman, Partitions and sums of (m,p,c)-sets, J. Comb. Theory (Series A) 45 (1987), 300–302.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    E. van Douwen, The Čech-Stone compactification of a discrete cancellative groupoid, manuscript.Google Scholar
  22. 22.
    R. Ellis, Lectures on topological dynamics, Benjamin, New York, 1969.zbMATHGoogle Scholar
  23. 23.
    Z. Frolík, Sums of ultrafilters, Bull. Amer. Math. Soc. 73 (1967), 87–91.MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    H. Furstenberg, Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions, J. d’Analyse Math. 31 (1977), 204–256.MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    H. Furstenberg, Recurrencee in ergodic theory and combinatorial number theory, Princeton University Press, Princeton, 1981.CrossRefzbMATHGoogle Scholar
  26. 26.
    L. Gillman and M. Jerison, Rings of continuous functions, van Nostrand, Princeeton, 1960.CrossRefzbMATHGoogle Scholar
  27. 27.
    S. Glasner, Divisibility properties and the Stone-Cech compactification, Canad. J. Math. 32 (1980), 993–1007.MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    N. Hindman, Minimal ideals and cancellation in βN, Semigroup Forum 25 (1982), 291–310.MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    N. Hindman, On density, translates, and pairwise sums of integers, J. Comb. Theory (Series A) 33 (1982), 147–157.MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    N. Hindman, Partitions and pairwise sums and products, J. Comb. Theory (Series A) 37 (1984), 46–60.MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    N. Hindman, Ramsey’s Theorem for sums, products and arithmetic progressions, J. Comb. Theory (Series A) 38 (1985), 82–83.MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    N. Hindman, Summable ultrafilters and finite sums, in Logic and Combinatorics, ed. S. Simpson, contemporary Mathematics 65 (1987), 263–274.MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    N. Hindman, Sums equal to products in βN, Semigroup Forum 21 (1980), 221–255.MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    N. Hindman, The existence of certain ultrafilters on N and a conjecture of Graham and Rothschild, Proc. Amer. Math. Soc. 36 (1972), 341–346.MathSciNetzbMATHGoogle Scholar
  35. 35.
    N. Hindman, The ideal structure of the space of κ-uniform ultrafilters on a discrete semigroup, Rocky Mountain J. Math. 16 (1986), 685–701.MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    N. Hindman, The minimal ideals of a multiplicative and additive subsemigroup of βN, Semigroup Forum 32 (1985), 283–292.MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    N. Hindman, Ultrafilters and combinatorial number theory, in Number Theory Carbondale 1979, ed. M. Nathanson, Lecture Notes in Math. 751 (1979), 119–184.MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    N. Hindman and P. Milnes, The LMC compactification of a topologized semigroup, Czech. Math. J., to appear.Google Scholar
  39. 39.
    N. Hindman and J. Pym, Free groups and semigroups in βN, Semigroup Forum 30 (1984), 177–193.MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    I. Kŕíž, Large independent sets in shift-invariant graphs. Solution of Bergelson’s problem, Graphs and Combinatorics 3 (1987), 145–158.MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    A. Lisan, Free groups in βN which miss the minimal ideal, Semigroup Forum, to appear.Google Scholar
  42. 42.
    P. Matet, Some filters of partitions, manuscript.Google Scholar
  43. 43.
    K. Milliken, Ramsey’s Theorem with sums or unions, J. Comb. Theory (Series A) 18 (1975), 276–290.MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    J. Pym, Semigroup structure in Stone-Cech compactifications, manuscript.Google Scholar
  45. 45.
    R. Raimi, Translation properties of finite partitions of the positive integers, Fund. Math. 61 (1968), 253–256.MathSciNetzbMATHGoogle Scholar
  46. 46.
    W. Rudin, Homogeneity problems in the theory of Cech compactifications, Duke Math. J. 23 (1956), 409–419.MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    W. Ruppert, In a left topological semigroup with dense center the closure of any left ideal is an ideal, Semigroup Forum, to appear.Google Scholar
  48. 48.
    W. Ruppert, Rechstopologische Halbgruppen, J. Reine Angew. Math. 261 (1973), 123–133.MathSciNetzbMATHGoogle Scholar
  49. 49.
    I. Ruzsa, Difference sets and the Bohr topology I., manuscript.Google Scholar
  50. 50.
    S. Shelah, Proper forcing, Lecture Notes in Math. 940 (1982).Google Scholar
  51. 51.
    E. Szemerédi, On sets of integers containing no k elements in arithmetic progression, Acta. Arith. 27 (1975), 199–245.MathSciNetzbMATHGoogle Scholar
  52. 52.
    A. Taylor, A canonical partition relation for finite subsets of ω, J. Comb. Theory (Series A) 21 (1976), 137–146.MathSciNetCrossRefzbMATHGoogle Scholar
  53. 53.
    H. Umoh, Ideals of the Stone-Cech compactification of semigroups, Semigroup Forum 32 (1985), 201–214.MathSciNetCrossRefzbMATHGoogle Scholar
  54. 54.
    H. Umoh, The ideal of products in βS\S, Dissertation, Howard University, 1987.Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  1. 1.Howard UniversityWashington, D.C.USA

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