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1

Strong meager properties for filters

100%

Laflamme C.

Fundamenta Mathematicae

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1994-1995

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tom 146

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nr 3

283-293

EN

We analyze several "strong meager" properties for filters on the natural numbers between the classical Baire property and a filter being $F_σ$. Two such properties have been studied by Talagrand and a few more combinatorial ones are investigated. In particular, we define the notion of a P⁺-filter, a generalization of the traditional concept of P-filter, and prove the existence of a non-meager P⁺-filter. Our motivation lies in understanding the structure of filters generated by complements of members of a maximal almost disjoint family.

2

Some possible covers of measure zero sets

100%

Laflamme C.

Colloquium Mathematicum

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1992

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tom 63

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nr 2

211-218

3

Filter games on ω and the dual ideal

63%

Laflamme C., Leary C.

Fundamenta Mathematicae

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2002

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tom 173

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nr 2

159-173

EN

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.

Ograniczanie wyników

2 Fundamenta Mathematicae

1 Colloquium Mathematicum

3 Laflamme C.

1 Leary C.

1 2002

1 1995

1 1992

Strong meager properties for filters

Some possible covers of measure zero sets

Filter games on ω and the dual ideal