The covering property for σ-ideals of compact, sets
Uzcátegui, Carlos
Fundamenta Mathematicae, Tome 141 (1992), p. 119-146 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

The covering property for σ-ideals of compact sets is an abstract version of the classical perfect set theorem for analytic sets. We will study its consequences using as a paradigm the σ-ideal of countable closed subsets of 2ω.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:211957 
@article{bwmeta1.element.bwnjournal-article-fmv141i2p119bwm,
     author = {Carlos Uzc\'ategui},
     title = {The covering property for $\sigma$-ideals of compact, sets},
     journal = {Fundamenta Mathematicae},
     volume = {141},
     year = {1992},
     pages = {119-146},
     zbl = {0799.04008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv141i2p119bwm}
}

Uzcátegui, Carlos. The covering property for σ-ideals of compact, sets. Fundamenta Mathematicae, Tome 141 (1992) pp. 119-146. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv141i2p119bwm/

[00000] [1] R. Barua and V. V. Srivatsa, Definable hereditary families in the projective hierarchy, Fund. Math. 140 (1992), 183-189. | Zbl 0809.04003

[00001] [2] G. Debs et J. Saint Raymond, Ensembles boréliens d'unicité et d'unicité au sens large, Ann. Inst. Fourier (Grenoble) 37 (3) (1987), 217-239. | Zbl 0618.42004

[00002] [3] A. S. Kechris, The theory of countable analytical sets, Trans. Amer. Math. Soc. 202 (1975), 259-297. | Zbl 0317.02082

[00003] [4] A. S. Kechris, On a notion of smallness for subsets of the Baire space, ibid. 229 (1977), 191-207.

[00004] [5] A. S. Kechris, Countable ordinals and the analytical hierarchy (II), Ann. Math. Logic 15 (1978), 193-223. | Zbl 0449.03047

[00005] [6] A. S. Kechris, The descriptive set theory of σ-ideals of compact sets, in: Logic Colloquium '88, R. Ferro, C. Bonotto, S. Valentini and A. Zanardo (eds.), North-Holland, 1979, 117-138.

[00006] [7] A. S. Kechris and A. Louveau, Descriptive Set Theory and the Structure of Sets of Uniqueness, London Math. Soc. Lecture Note Ser. 128, Cambridge Univ. Press, 1987. | Zbl 0642.42014

[00007] [8] A. S. Kechris, A. Louveau and W. H. Woodin, The structure of σ-ideals of compact sets, Trans. Amer. Math. Soc. 301 (1987), 263-288. | Zbl 0633.03043

[00008] [9] A. Louveau, σ-idéaux engendrés par des ensembles fermés et théorèmes d'approximation, ibid. 257 (1980), 143-169.

[00009] [10] D. A. Martin and A. S. Kechris, Infinite games and effective descriptive set theory, in: Analytic Sets, by C. A. Rogers et al., Academic Press, 1980, 403-499.

[00010] [11] Y. N. Moschovakis, Descriptive Set Theory, North-Holland, Amsterdam 1980.

[00011] [12] J. Oxtoby, Measure and Category, Springer, New York 1971.