ArticleOriginal scientific text
Title
The covering property for σ-ideals of compact, sets
Authors 1
Affiliations
- Departamento de Matemáticas, Facultad de Ciencias, Universidad de Los Andes, Mérida 5101, Venezuela
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 .
Bibliography
- R. Barua and V. V. Srivatsa, Definable hereditary families in the projective hierarchy, Fund. Math. 140 (1992), 183-189.
- 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.
- A. S. Kechris, The theory of countable analytical sets, Trans. Amer. Math. Soc. 202 (1975), 259-297.
- A. S. Kechris, On a notion of smallness for subsets of the Baire space, ibid. 229 (1977), 191-207.
- A. S. Kechris, Countable ordinals and the analytical hierarchy (II), Ann. Math. Logic 15 (1978), 193-223.
- 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.
- 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.
- 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.
- A. Louveau, σ-idéaux engendrés par des ensembles fermés et théorèmes d'approximation, ibid. 257 (1980), 143-169.
- 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.
- Y. N. Moschovakis, Descriptive Set Theory, North-Holland, Amsterdam 1980.
- J. Oxtoby, Measure and Category, Springer, New York 1971.
Additional information
http://matwbn.icm.edu.pl/ksiazki/fm/fm141/fm14123.pdf