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Trichotomies for ideals of compact sets

Published online by Cambridge University Press:  12 March 2014

É. Matheron ,
S. Solecki  and
M. Zelený
É. Matheron
Affiliation:
Université Bordeaux 1, 351 Cours de la Libération, 33405 Talence Cedex, France. E-mail: Etienne.Matheron@math.u-bordeauxl.fr
S. Solecki
Affiliation:
Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, IL 61801, USA. E-mail: ssolecki@math.uiuc.edu
M. Zelený
Affiliation:
Charles University, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Sokolovská 83, Prague 8, 186 75, Czech Republic. E-mail: zeleny@karlin.mff.cuni.cz
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Abstract

We prove several trichotomy results for ideals of compact sets. Typically, we show that a “sufficiently rich” universally Baire ideal is either Π30-hard. or Σ30-hard. or else a σ-ideal.

Keywords

ideals of compact setsdescriptive set theory
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 2 , June 2006 , pp. 586 - 598
Copyright
Copyright © Association for Symbolic Logic 2006

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References

REFERENCES

[BD]Balcerzak, M. and Darji, U. B.. Some examples of true Fσδ sets, Colloquium Mathematicum, vol. 86 (2000), pp. 203–207.CrossRefGoogle Scholar
[C]Christensen, J. P. R.. Topology and Borel structure. North-Holland Mathematics Studies, vol. 10. (Notasde Matemática 51). North-Holland/Elsevier, Amsterdam, 1974.Google Scholar
[DSR]Debs, G. and Saint-Raymond, J.. Ensembles boréliens d'unicité et d'unicité au sens large, Annates de l'Institut Fourier, vol. 37 (1987), no. 3. pp. 217–239. Université de Grenoble.CrossRefGoogle Scholar
[K2]Kechris, A. S., Hereditary properties of the class of closed sets of uniqueness for trigonometric series, Israel Journal of Mathematics, vol. 73 (1991), pp. 189–198.CrossRefGoogle Scholar
[K1]Kechris, A. S., Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag. 1995.CrossRefGoogle Scholar
[KL]Kechris, A. S. and Louveau, A.. Descriptive set theory and the structure of sets of uniqueness, London Mathematical Society Lecture Note Series, vol. 128. Cambridge University Press, Cambridge, 1987.CrossRefGoogle Scholar
[KLW]Kechris, A. S., Louveau, A., and Woodin, W. H.. The structure of σ-ideals of compact sets, Transactions of the American Mathematical Society, vol. 301 (1987). pp. 263–288.Google Scholar
[M]Matheron, É., How to recognize a true set. Fundamenta Mathematical vol. 158 (1998), pp. 181–194.CrossRefGoogle Scholar
[MZ]Matheron, É. and Zelený, M.. Rudin-like sets and hereditary families of compact sets, Fundamenta Mathematical vol, 185 (2005), pp. 97–116.CrossRefGoogle Scholar
[ST]Solecki, S. and Todorcevic, S.. Cofinal types of topological directed orders, Annates de l'Institut Fourier, vol. 54 (2004). pp. 1877–1911. Université de Grenoble.Google Scholar
[T]Todorcevic, S.. Topics in topology. Lecture Notes in Mathematics, vol. 1652. Springer-Verlag, Berlin, 1997.CrossRefGoogle Scholar
[E]van Engelen, F., On borel ideals, Annals of Pure and Applied Logic, vol. 70 (1994). pp. 177–203.CrossRefGoogle Scholar