Strong meager properties for filters

• Autorzy: Claude Laflamme
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

filter; meager; Baire property

Kategorie tematyczne

• 03E05: Other combinatorial set theory
• 03E15: Descriptive set theory
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994-1995
• Tom: 146
• Numer: 3
• Strony: 283-293

Daty

wydano

1995

otrzymano

1993-12-07

poprawiono

1994-11-07

Twórcy

autor

Claude Laflamme

• 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.