Abstract
We construct a nonmeager ideal that is not a P-ideal yet Fin × ⊘ is not reducible to it.
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References
M. Hrušák, MAD Families and the Rationals, preprint (2000).
S.-A. Jalali-Naini, The Monotone Subsets of Cantor Space, Filters and Descriptive Set Theory, Ph.D. Thesis, Oxford (1976).
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).
C. Laflamme, “Strong meager properties for filters,” Fund. Math., 146, 283–293 (1995).
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.
S. Solecki, “Analytic ideals,” Bull. Symbolic Logic, 2, 339–348 (1996).
S. Solecki, “Analytic ideals and their applications,” Ann. Pure Appl. Logic, 99, 51–72 (1999).
S. Solecki, “Filters and sequences,” Fund. Math., 163, 215–228 (2000).
R. Solovay, “A model of set theory in which every set of reals is Lebesgue measurable,” Ann. Math., 92, 1–56 (1970).
M. Talagrand, “Compacts de fonctions mesurables et filters nonmesurables,” Stud. Math., 67, 13–43 (1980).
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.
J. Zapletal, “The nonstationary ideal and the other σ-ideals on ω,” Trans. Amer. Math. Soc., 352, No. 9, 3981–3993 (2000).
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 213–219, 2005.
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Farah, I. Reductions between meager ideals. J Math Sci 144, 4511–4515 (2007). https://doi.org/10.1007/s10958-007-0290-3
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DOI: https://doi.org/10.1007/s10958-007-0290-3