Strong meager properties for filters

1993/12/14 by Claude Laflamme, Laflamme, Claude
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.math/9312204

arxiv created 1993/12/14 · arxiv updated 2009/11/30

Abstract

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.

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