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Countable Borel Equivalence Relations II Simon Thomas
 

Summary: Countable Borel Equivalence Relations II
Simon Thomas
Rutgers University
17th November 2007
Simon Thomas (Rutgers University) Appalachian Set Theory Workshop 17th November 2007
A quick recap
Theorem (Feldman-Moore)
If E is a countable Borel equivalence relation on the standard Borel
space X, then there exists a countable group G and a Borel action
of G on X such that E = EX
G .
Warning
The proof of the Feldman-Moore Theorem does not produce a
"canonical group action".
It is sometimes difficult to express a countable Borel equivalence
relation as the orbit equivalence relation arising from a "natural
action." Cf. the Turing equivalence relation.
Simon Thomas (Rutgers University) Appalachian Set Theory Workshop 17th November 2007
Comparing orbit equivalence relations
Stating the obvious

  

Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University

 

Collections: Mathematics