Filter games on $\omega $ and the dual ideal

Tom 173 / 2002

Claude Laflamme, Christopher C. Leary Fundamenta Mathematicae 173 (2002), 159-173 MSC: Primary 03E05; Secondary 03E15, 03E35. DOI: 10.4064/fm173-2-4


We continue the efforts to characterize winning strategies in various infinite games involving filters on the natural numbers in terms of combinatorial or structural properties of the given filter. Previous results in the literature included those games where player II responded with natural numbers, or finite subsets of natural numbers. In this paper we concentrate on games where player II responds with members of the dual ideal. We also give a summary of known results on filter games.


  • Claude LaflammeDepartment of Mathematics and Statistics
    University of Calgary
    Calgary, Alberta
    Canada T2N 1N4
  • Christopher C. LearyDepartment of Mathematics
    SUNY Geneseo
    Geneseo, NY 14454, U.S.A.

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