Regularity and Positional Games

  • A.Ā W.Ā Hales
  • R.I.Ā Jewett
Part of the Modern BirkhƤuser Classics book series (MBC)


1.Introduction. Suppose X is a set, š¯’˛ a collection of sets (usually subsets of X), and N is cardinal number. Following the terminology of Rado [1], we say š¯’˛ is N-regular in X if,for any partition of X into N parts, some part has as a subset a member of š¯’˛. if š¯’˛ is n-regular in X for each integer n, we say š¯’˛ is regular in X.


Choice FunctionĀ Finite SubsetĀ Arithmetic ProgressionĀ Cardinal NumberĀ Commutative SemigroupĀ 
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  1. 1.
    R. Rado, Note on combinatorial analysis, Proc. London Math. Soe. (2) 48 (1943-45), 122ā€“160.Google Scholar
  2. 2.
    A. Y. Khinchin, Three pearls of number theory, Graylock Press, Rochester, 1952, pp. 11ā€“12MATHGoogle Scholar
  3. 3.
    R. Rado, Axiomatic treatment of rank in infinite sets, Canad. J. Math. 1 (1949), 338.MathSciNetGoogle Scholar
  4. 4.
    W. H. Gottschalk, Choice functions and Tychonoffā€™s Theorem, Proc. Amer. Math. Soc. 2(1951), 172.Google Scholar
  5. 5.
    D. Blackwell and M. A. Girshick, Theory of games and statistical decisions, Wiley, New York, 1954, p. 21.MATHGoogle Scholar
  6. 6.
    P. Hall, On representatives of subsets, J. London Math. Soc, 10 (1935), 26ā€“30.MATHCrossRefGoogle Scholar

Copyright information

Ā©Ā BirkhƤuser Boston, a part of Springer Science+Business Media, LLCĀ 2009

Authors and Affiliations

  • A.Ā W.Ā Hales
    • 1
  • R.I.Ā Jewett
    • 2
  1. 1.California Institute of TechnologyPasadenaUSA
  2. 2.University of OregonEugeneUSA

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