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Regularity and Positional Games

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

Abstract

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.

Keywords

Choice FunctionĀ Finite SubsetĀ Arithmetic ProgressionĀ Cardinal NumberĀ Commutative SemigroupĀ 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    R. Rado, Note on combinatorial analysis, Proc. London Math. Soe. (2) 48 (1943-45), 122ā€“160.Google Scholar
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    R. Rado, Axiomatic treatment of rank in infinite sets, Canad. J. Math. 1 (1949), 338.MathSciNetGoogle Scholar
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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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