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ISSN 1079-6762

 

Hurewicz-like tests for Borel subsets of the plane


Author: Dominique Lecomte
Journal: Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 95-102
MSC (2000): Primary 03E15; Secondary 54H05
Published electronically: December 15, 2005
MathSciNet review: 2191690
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Abstract: Let $ \xi \geq 1$ be a countable ordinal. We study the Borel subsets of the plane that can be made $ \boldsymbol \Pi ^{0}_{\xi }$ by refining the Polish topology on the real line. These sets are called potentially $ \boldsymbol \Pi ^{0}_{\xi }$. We give a Hurewicz-like test to recognize potentially $ \boldsymbol \Pi ^{0}_{\xi }$ sets.


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Additional Information

Dominique Lecomte
Affiliation: Université Paris 6, Equipe d’Analyse Fonctionnelle, tour 46-0, boîte 186, 4, place Jussieu, 75 252 Paris Cedex 05, France, and Université de Picardie, I.U.T. de l’Oise, site de Creil, 13, allée de la faïencerie, 60 107 Creil, France
Email: lecomte@moka.ccr.jussieu.fr

DOI: http://dx.doi.org/10.1090/S1079-6762-05-00152-6
PII: S 1079-6762(05)00152-6
Keywords: Potentially, Baire classes, reduction, Hurewicz's Theorem
Received by editor(s): July 29, 2005
Published electronically: December 15, 2005
Communicated by: Alexander Kechris
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.