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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Compact covering mappings between Borel sets and the size of constructible reals


Authors: Gabriel Debs and Jean Saint Raymond
Journal: Trans. Amer. Math. Soc. 356 (2004), 73-117
MSC (2000): Primary 03E15; Secondary 03E45, 54H05
Published electronically: August 25, 2003
MathSciNet review: 2020025
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Abstract: We prove that the topological statement: ``Any compact covering mapping between two Borel sets is inductively perfect" is equivalent to the set-theoretical statement: $\lq\lq \,\forall\alpha\in \omega^\omega,\; \aleph_1^{L(\alpha)}<\aleph_1$".


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Additional Information

Gabriel Debs
Affiliation: Analyse Fonctionnelle, Institut de Mathématique de Jussieu, Boîte 186, 4, place Jussieu, 75252 Paris Cedex 05, France
Email: gad@ccr.jussieu.fr

Jean Saint Raymond
Affiliation: Analyse Fonctionnelle, Institut de Mathématique de Jussieu, Boîte 186, 4, place Jussieu, 75252 Paris Cedex 05, France
Email: jsr@ccr.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03206-9
PII: S 0002-9947(03)03206-9
Received by editor(s): May 31, 2001
Published electronically: August 25, 2003
Article copyright: © Copyright 2003 American Mathematical Society