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Analytic Equivalence Relations and the Forcing Method

Published online by Cambridge University Press:  05 September 2014

Jindřich Zapletal
Jindřich Zapletal*
Affiliation:
Institute of Mathematics, Academy of Sciences ŽItná 25 11567 Praha 1, Czech Republic Department of Mathematics, University of Florida, Gainesville, FL 32611, USA, E-mail: [email protected]
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Abstract

I describe several ways in which forcing arguments can be used to yield clean and conceptual proofs of nonreducibility, ergodicity and other results in the theory of analytic equivalence relations. In particular, I present simple Borel equivalence relations E, F such that a natural proof of nonreducibility of E to F uses the independence of the Singular Cardinal Hypothesis at ℵω.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 19 , Issue 4 , September 2013 , pp. 473 - 490
Copyright
Copyright © Association for Symbolic Logic 2013

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