Property τ and countable borel equivalence relations

Journal of Mathematical Logic 7 (1):1-34 (2007)
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Abstract

We prove Borel superrigidity results for suitably chosen actions of groups of the form SL2, where {p1, …, pt} is a finite nonempty set of primes, and present a number of applications to the theory of countable Borel equivalence relations. In particular, for each prime q, we prove that the orbit equivalence relations arising from the natural actions of SL2 on the projective lines ℚp ∪ {∞}, p ≠ q, over the various p-adic fields are pairwise incomparable with respect to Borel reducibility.

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Countable borel equivalence relations.S. Jackson, A. S. Kechris & A. Louveau - 2002 - Journal of Mathematical Logic 2 (01):1-80.
Superrigidity and countable Borel equivalence relations.Simon Thomas - 2003 - Annals of Pure and Applied Logic 120 (1-3):237-262.

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