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Cofinal families of Borel equivalence relations and quasiorders

Published online by Cambridge University Press:  12 March 2014

Christian Rosendal
Christian Rosendal*
Affiliation:
Department of Mathematics, University of Illinois at Urbana, 273 Altgeld Hall, MC-382, 1409 West Greet Street, Urbana, IL 61801, USA, E-mail: rosendal@ccr.jussieu.fr
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Abstract

Families of Borel equivalence relations and quasiorders that are cofinal with respect to the Borel reducibility ordering. ≤B, are constructed. There is an analytic ideal on ω generating a complete analytic equivalence relation and any Borel equivalence relation reduces to one generated by a Borel ideal. Several Borel equivalence relations, among them Lipschitz isomorphism of compact metric spaces, are shown to be Kσ complete.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 4 , December 2005 , pp. 1325 - 1340
Copyright
Copyright © Association for Symbolic Logic 2005

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