# The covering property for σ-ideals of compact, sets

Fundamenta Mathematicae (1992)

- Volume: 141, Issue: 2, page 119-146
- ISSN: 0016-2736

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topUzcátegui, Carlos. "The covering property for σ-ideals of compact, sets." Fundamenta Mathematicae 141.2 (1992): 119-146. <http://eudml.org/doc/211957>.

@article{Uzcátegui1992,

abstract = {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 $2^ω$.},

author = {Uzcátegui, Carlos},

journal = {Fundamenta Mathematicae},

keywords = {ideals of compact sets; metric space; covering property},

language = {eng},

number = {2},

pages = {119-146},

title = {The covering property for σ-ideals of compact, sets},

url = {http://eudml.org/doc/211957},

volume = {141},

year = {1992},

}

TY - JOUR

AU - Uzcátegui, Carlos

TI - The covering property for σ-ideals of compact, sets

JO - Fundamenta Mathematicae

PY - 1992

VL - 141

IS - 2

SP - 119

EP - 146

AB - 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 $2^ω$.

LA - eng

KW - ideals of compact sets; metric space; covering property

UR - http://eudml.org/doc/211957

ER -

## References

top- [1] R. Barua and V. V. Srivatsa, Definable hereditary families in the projective hierarchy, Fund. Math. 140 (1992), 183-189. Zbl0809.04003
- [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. Zbl0618.42004
- [3] A. S. Kechris, The theory of countable analytical sets, Trans. Amer. Math. Soc. 202 (1975), 259-297. Zbl0317.02082
- [4] A. S. Kechris, On a notion of smallness for subsets of the Baire space, ibid. 229 (1977), 191-207.
- [5] A. S. Kechris, Countable ordinals and the analytical hierarchy (II), Ann. Math. Logic 15 (1978), 193-223. Zbl0449.03047
- [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.
- [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. Zbl0642.42014
- [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. Zbl0633.03043
- [9] A. Louveau, σ-idéaux engendrés par des ensembles fermés et théorèmes d'approximation, ibid. 257 (1980), 143-169.
- [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.
- [11] Y. N. Moschovakis, Descriptive Set Theory, North-Holland, Amsterdam 1980.
- [12] J. Oxtoby, Measure and Category, Springer, New York 1971.

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