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Summary: Countable Borel Equivalence Relations IV
Simon Thomas
Rutgers University
17th November 2007
Simon Thomas (Rutgers University) Appalachian Set Theory Workshop 17th November 2007
An application of Ioana Superrigidity
The Kechris Conjecture
T is universal.
Observation
There exists a universal countable Borel equivalence relation E on
P(N) such that E T .
Proof.
Identifying the free group F2 with a suitably chosen group of recursive
permutations of N, we have that E T .
Simon Thomas (Rutgers University) Appalachian Set Theory Workshop 17th November 2007
An application of Ioana Superrigidity
Conjecture (Hjorth)
If F is a universal countable Borel equivalence relation on the standard
Borel space X and E is a countable Borel equivalence relation such
that F E, then E is also universal.
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