Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
283-293
Opis fizyczny
Daty
wydano
1995
otrzymano
1993-12-07
poprawiono
1994-11-07
Twórcy
autor
- Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta Canada T2N 1N4
Bibliografia
- [1] T. Bartoszyński and H. Judah, Measure and category - filters on ω, in: Set Theory of the Continuum, H. Judah, W. Just and H. Woodin (eds.), Springer, 1992, 175-201.
- [2] W. Just, A. R. D. Mathias, K. Prikry and P. Simon, On the existence of large P-ideals, J. Symbolic Logic 55 (1990), 457-465.
- [3] C. Laflamme, Zapping small filters, Proc. Amer. Math. Soc. 114 (1992), 535-544.
- [4] S. Shelah, Cardinal invariants of the continuum, in: Axiomatic Set Theory, J. Baumgartner, D. Martin and S. Shelah (eds.), Contemp. Math. 31, Amer. Math. Soc., 1984, 183-207.
- [5] P. Simon, private communication, August 1987.
- [6] M. Talagrand, Compacts de fonctions mesurables et filtres non mesurables, Studia Math. 67 (1980), 13-43.
- [7] M. Talagrand, Filtres: mesurabilité, rapidité, propriété de Baire forte, ibid. 74 (1982), 283-291.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv146i3p283bwm