We analyze several “strong meager” properties for filters on the natural numbers between the classical Baire property and a filter being . 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.
@article{bwmeta1.element.bwnjournal-article-fmv146i3p283bwm,
author = {Claude Laflamme},
title = {Strong meager properties for filters},
journal = {Fundamenta Mathematicae},
volume = {146},
year = {1995},
pages = {283-293},
zbl = {0839.03033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv146i3p283bwm}
}
Laflamme, Claude. Strong meager properties for filters. Fundamenta Mathematicae, Tome 146 (1995) pp. 283-293. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv146i3p283bwm/
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