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Filter games on \(\omega\) and the dual ideal. (English) Zbl 0998.03038
Summary: 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.

MSC:
03E05 Other combinatorial set theory
91A44 Games involving topology, set theory, or logic
03E35 Consistency and independence results
03E15 Descriptive set theory
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