ArticleOriginal scientific text

Title

The covering property for σ-ideals of compact, sets

Authors 1

Affiliations

  1. 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 2ω.

Bibliography

  1. R. Barua and V. V. Srivatsa, Definable hereditary families in the projective hierarchy, Fund. Math. 140 (1992), 183-189.
  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.
  3. A. S. Kechris, The theory of countable analytical sets, Trans. Amer. Math. Soc. 202 (1975), 259-297.
  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.
  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.
  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.
  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.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm141/fm14123.pdf

Pages:
119-146
Main language of publication
English
Received
1991-02-11
Accepted
1992-02-11
Published
1992
Exact and natural sciences