On the uniqueness of measure and category σ-ideals on 2^ω

• Autorzy: Zakrzewski P.
• Języki publikacji: EN

Abstrakty

EN

We prove that if <I,J> of ccc, translation invariant σ-ideals on 2<sup>ω has the Fubini Property, then I = J. This leads to a slightly impoved exposition of a part of the Farah-Zapletal proof of an invariant version of their theorem which characterizes the measure and category σ-ideals on 2<sup>ω as essentially the only ccc definable σ-ideals with Fubini Property.

Słowa kluczowe

EN

σ-ideals; Fubini property; measure and category ideals

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2007
• Tom: Vol. 13, nr 2
• Strony: 249--257
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Zakrzewski P.

• Institute of Mathematics University of Warsaw, Banacha 2, 02-097 Warsaw, Poland,

Bibliografia

• [1] Balcar, B. Jech, T., Weak distributivity, a problem of von Neumann and the mystery of measurability, Bull. Symbolic Logic 2 (2006), 241-266.
• [2] Balcar, B., Jech, T., Pazak, T., Complete ccc Boolean algebras, the order sequential topology and a problem of von Neumann, Bull. London Math. Soc. 37 (2005), 885-898.
• [3] Bartoszyński, T., Judah, H., Set Theory. On the Structure of the Real Line, A K Peters, Ltd., Wellesley, MA, 1995.
• [4] Farah, I., Zapletal, J., Between Mahamm and von Neumann's problems, Math. Res. Lett. 11(5-6) (2004), 673-684.
• [5] Kechris, A. S., Classical Descriptive Set Theory, Grad. Texts in Math. 156, Springer-Verlag; New York, 1995.
• [6] Kechris, A. S., Louveau, A., Woodin, W. H., The structure of σ-ideals of compact sets, Trans. Amer. Math. Soc. 301(1) (1987), 263-288.
• [7] Kunen, K., Random and Cohen Teals, in: "Handbook of Set-Theoretic Topology", K. Kumen and J. Vaughan (Eds.), North Holland, Amsterdam, 1984, 887-911.
• [8] Miller, A., A hodgepodge of sets of Teals, Note Mat., (to appear) http://www.math.wisc.edu/ miller/res/podge.pdf.
• [9] Recław, I., Zakrzewski, P., Fubini properties of ideals, Real Anal. Exchange 25(2) (1999/00), 565-578.
• [10] Rosłanowski, A., Shelah, S., Norms on, possibilities II: more ccc ideals on 2nd, J. Appl. Anal. 3 (1997), 103-127.
• [11] Shelah, S., How special are Cohen and random forcings i.e. Boolean algebras of the family of subsets of Teals modulo meagre or null, Israel J. Math. 88 (1994), 159-174.
• [12] Talagrand, M., Maharam's problem, Ann. of Math. (2), (to appear) http://arxiv.org/PS_cache/math/pdf/0601/0601689.pdf.
• [13] Zapletal, J., Forcing Idealized, a book in preparation to be published by Cambridge University Press (2007), available at http://www.math.ufl.edu/zapletal/main.pdf.
• [14] Zakrzewski, P., Fubini properties for filter-related σ-ideals, Topology Appl. 136(1-3)(2004), 239-249.