Strong meager properties for filters

Claude Laflamme

Fundamenta Mathematicae (1995)

  • Volume: 146, Issue: 3, page 283-293
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Laflamme, Claude. "Strong meager properties for filters." Fundamenta Mathematicae 146.3 (1995): 283-293. <http://eudml.org/doc/212067>.

@article{Laflamme1995,
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.},
author = {Laflamme, Claude},
journal = {Fundamenta Mathematicae},
keywords = {filter; meager; Baire property; meager sets; forcing; filters; 0-1 sequences; topology},
language = {eng},
number = {3},
pages = {283-293},
title = {Strong meager properties for filters},
url = {http://eudml.org/doc/212067},
volume = {146},
year = {1995},
}

TY - JOUR
AU - Laflamme, Claude
TI - Strong meager properties for filters
JO - Fundamenta Mathematicae
PY - 1995
VL - 146
IS - 3
SP - 283
EP - 293
AB - 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.
LA - eng
KW - filter; meager; Baire property; meager sets; forcing; filters; 0-1 sequences; topology
UR - http://eudml.org/doc/212067
ER -

References

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  1. [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. Zbl0787.03036
  2. [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. Zbl0715.04002
  3. [3] C. Laflamme, Zapping small filters, Proc. Amer. Math. Soc. 114 (1992), 535-544. Zbl0746.04002
  4. [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. [5] P. Simon, private communication, August 1987. 
  6. [6] M. Talagrand, Compacts de fonctions mesurables et filtres non mesurables, Studia Math. 67 (1980), 13-43. Zbl0435.46023
  7. [7] M. Talagrand, Filtres: mesurabilité, rapidité, propriété de Baire forte, ibid. 74 (1982), 283-291. Zbl0503.04003

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