On c-sets and products of ideals

• Autorzy: Marek Balcerzak
• Języki publikacji: EN

Abstrakty

EN

Let X, Y be uncountable Polish spaces and let μ be a complete σ-finite Borel measure on X. Denote by K and L the families of all meager subsets of X and of all subsets of Y with μ measure zero, respectively. It is shown that the product of the ideals K and L restricted to C-sets of Selivanovskiĭ is σ-saturated, which extends Gavalec's results.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1991
• Tom: 62
• Numer: 1
• Strony: 1-6

Daty

wydano

1991

otrzymano

1988-05-10

poprawiono

1990-02-23

Twórcy

autor

Marek Balcerzak

• Institute of Mathematics, Łódź University, S. Banacha 22, 90-238 Łódź, Poland

Bibliografia

• [1] M. Balcerzak, Remarks on products of σ-ideals, Colloq. Math. 56 (1988), 201-209.
• [2] J. P. Burgess, Classical hierarchies from a modern stand-point, Part I, C-sets, Fund. Math. 115 (1983), 80-95.
• [3] D. Cenzer and R. D. Mauldin, Inductive definability: measure and category, Adv. in Math. 38 (1980), 55-90.
• [4] J. Cichoń and J. Pawlikowski, On ideals of subsets of the plane and on Cohen reals, J. Symbolic Logic 51 (1986), 560-569.
• [5] M. Gavalec, Iterated products of ideals of Borel sets, Colloq. Math. 50 (1985), 39-52.
• [6] A. S. Kechris, Measure and category in effective descriptive set theory, Ann. Math. Logic 5 (1972/73), 337-384.
• [7] C. G. Mendez, On sigma-ideals of sets, Proc. Amer. Math. Soc. 60 (1976), 124-128.
• [8] Y. N. Moschovakis, Descriptive Set Theory, North-Holland, Amsterdam 1980.
• [9] E. A. Selivanovskiĭ, On a class of effective sets (C-sets), Mat. Sb. 35 (1928), 379-413 (in Russian).
• [10] V. V. Srivatsa, Measure and category approximations for C-sets, Trans. Amer. Math. Soc. 278 (1983), 495-505.
• [11] R. L. Vaught, Invariant sets in topology and logic, Fund. Math. 82 (1974), 269-294.