# On c-sets and products of ideals

Colloquium Mathematicae (1991)

- Volume: 62, Issue: 1, page 1-6
- ISSN: 0010-1354

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topBalcerzak, Marek. "On c-sets and products of ideals." Colloquium Mathematicae 62.1 (1991): 1-6. <http://eudml.org/doc/210094>.

@article{Balcerzak1991,

abstract = {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.},

author = {Balcerzak, Marek},

journal = {Colloquium Mathematicae},

keywords = {products of ideals; Polish spaces; -finite Borel measure; - sets; -saturated},

language = {eng},

number = {1},

pages = {1-6},

title = {On c-sets and products of ideals},

url = {http://eudml.org/doc/210094},

volume = {62},

year = {1991},

}

TY - JOUR

AU - Balcerzak, Marek

TI - On c-sets and products of ideals

JO - Colloquium Mathematicae

PY - 1991

VL - 62

IS - 1

SP - 1

EP - 6

AB - 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.

LA - eng

KW - products of ideals; Polish spaces; -finite Borel measure; - sets; -saturated

UR - http://eudml.org/doc/210094

ER -

## References

top- [1] M. Balcerzak, Remarks on products of σ-ideals, Colloq. Math. 56 (1988), 201-209. Zbl0679.28003
- [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. Zbl0466.03018
- [4] J. Cichoń and J. Pawlikowski, On ideals of subsets of the plane and on Cohen reals, J. Symbolic Logic 51 (1986), 560-569. Zbl0622.03035
- [5] M. Gavalec, Iterated products of ideals of Borel sets, Colloq. Math. 50 (1985), 39-52. Zbl0604.28001
- [6] A. S. Kechris, Measure and category in effective descriptive set theory, Ann. Math. Logic 5 (1972/73), 337-384. Zbl0277.02019
- [7] C. G. Mendez, On sigma-ideals of sets, Proc. Amer. Math. Soc. 60 (1976), 124-128. Zbl0348.28002
- [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. Zbl0525.04006
- [11] R. L. Vaught, Invariant sets in topology and logic, Fund. Math. 82 (1974), 269-294. Zbl0309.02068

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