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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A remark on the Debs-Saint-Raymond theorem


Author: Miroslav Zelený
Journal: Proc. Amer. Math. Soc. 129 (2001), 3711-3714
MSC (2000): Primary 03E15, 28A05, 54H05
Published electronically: April 24, 2001
MathSciNet review: 1860506
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Abstract:

A theorem of Debs and Saint-Raymond gives sufficient conditions for a $\sigma $-ideal of compact sets to have the covering property. We discuss the necessity of these conditions. Namely, we show that there exists a $\boldsymbol \Pi _{\mathbf{1}}^{\mathbf{1}}$ $\sigma $-ideal that is locally non-Borel, has no Borel basis and has the covering property. This partially answers a question posed by Kechris.


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Additional Information

Miroslav Zelený
Affiliation: Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 186 00, Czech Republic
Email: zeleny@karlin.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05978-0
PII: S 0002-9939(01)05978-0
Received by editor(s): January 7, 2000
Received by editor(s) in revised form: April 9, 2000
Published electronically: April 24, 2001
Additional Notes: The author’s research was supported by GAUK 190/1996, GAČR 201/97/1161, and CEZ J13/98113200007
Communicated by: Alan Dow
Article copyright: © Copyright 2001 American Mathematical Society