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Complete analytic equivalence relations


Authors: Alain Louveau and Christian Rosendal
Journal: Trans. Amer. Math. Soc. 357 (2005), 4839-4866
MSC (2000): Primary 03E15
DOI: https://doi.org/10.1090/S0002-9947-05-04005-5
Published electronically: July 19, 2005
MathSciNet review: 2165390
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Abstract: We prove that various concrete analytic equivalence relations arising in model theory or analysis are complete, i.e. maximum in the Borel reducibility ordering. The proofs use some general results concerning the wider class of analytic quasi-orders.


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Additional Information

Alain Louveau
Affiliation: Equipe d’Analyse Fonctionnelle, Institut de Mathématiques, Université Pierre et Marie Curie - Paris 6, Boîte 186, 4 Place Jussieu, 75252 Paris Cedex 05, France
Email: louveau@ccr.jussieu.fr

Christian Rosendal
Affiliation: Equipe d’Analyse Fonctionnelle, Institut de Mathématiques, Université Pierre et Marie Curie - Paris 6, Boîte 186, 4 Place Jussieu, 75252 Paris Cedex 05, France
Address at time of publication: Mathematics 253-37, Caltech, Pasadena, California 91125
Email: rosendal@ccr.jussieu.fr

DOI: https://doi.org/10.1090/S0002-9947-05-04005-5
Keywords: Definable equivalence relations, descriptive set theory
Received by editor(s): May 14, 2003
Published electronically: July 19, 2005
Article copyright: © Copyright 2005 American Mathematical Society

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