Skip to main content

Reductions between meager ideals


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, access via your institution.


  1. 1.

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

  2. 2.

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

  3. 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).

    MATH  Article  Google Scholar 

  4. 4.

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

    MATH  Google Scholar 

  5. 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. 6.

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

    MATH  Article  Google Scholar 

  7. 7.

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

    MATH  Article  Google Scholar 

  8. 8.

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

    MATH  Google Scholar 

  9. 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. 10.

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

    MATH  Google Scholar 

  11. 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. 12.

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

    MATH  Article  Google Scholar 

Download references

Author information



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).

Download citation


  • Large Cardinal
  • Analytic Ideal
  • Baire Property
  • Cantor Space
  • Monotone Subset