Strong meager properties for filters

Tom 146 / 1995

Claude Laflamme Fundamenta Mathematicae 146 (1995), 283-293 DOI: 10.4064/fm-146-3-283-293


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.


  • Claude Laflamme

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