Skip to main content
SpringerLink
Log in

Reductions between meager ideals

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

We construct a nonmeager ideal that is not a P-ideal yet Fin × ⊘ is not reducible to it.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Hrušák, MAD Families and the Rationals, preprint (2000).

  2. S.-A. Jalali-Naini, The Monotone Subsets of Cantor Space, Filters and Descriptive Set Theory, Ph.D. Thesis, Oxford (1976).

  3. W. Just, A. R. D. Mathias, K. Prikry, and P. Simon, “On the existence of large p-ideals,” J. Symbolic Logic, 55, 457–465 (1990).

    Article  MATH  Google Scholar 

  4. C. Laflamme, “Strong meager properties for filters,” Fund. Math., 146, 283–293 (1995).

    MATH  Google Scholar 

  5. A. R. D. Mathias, “A remark on rare filters,” in: A. Hajnal et al., eds., Infinite and Finite Sets, Vol. III, North-Holland (1975), Coll. Math. Soc. Janos Bolyai, Vol. 10, pp. 1095–1097.

  6. S. Solecki, “Analytic ideals,” Bull. Symbolic Logic, 2, 339–348 (1996).

    Article  MATH  Google Scholar 

  7. S. Solecki, “Analytic ideals and their applications,” Ann. Pure Appl. Logic, 99, 51–72 (1999).

    Article  MATH  Google Scholar 

  8. S. Solecki, “Filters and sequences,” Fund. Math., 163, 215–228 (2000).

    MATH  Google Scholar 

  9. R. Solovay, “A model of set theory in which every set of reals is Lebesgue measurable,” Ann. Math., 92, 1–56 (1970).

    Article  Google Scholar 

  10. M. Talagrand, “Compacts de fonctions mesurables et filters nonmesurables,” Stud. Math., 67, 13–43 (1980).

    MATH  Google Scholar 

  11. S. Todorcevic, “Definable ideals and gaps in their quotients,” in: C. A. DiPrisco et al., eds., Set Theory: Techniques and Applications, Kluwer Academic (1997), pp. 213–226.

  12. J. Zapletal, “The nonstationary ideal and the other σ-ideals on ω,” Trans. Amer. Math. Soc., 352, No. 9, 3981–3993 (2000).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3, Canada

    Ilijas Farah

Authors
  1. Ilijas Farah
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 213–219, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Farah, I. Reductions between meager ideals. J Math Sci 144, 4511–4515 (2007). https://doi.org/10.1007/s10958-007-0290-3

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-007-0290-3

Keywords

Search

Navigation