School of Mathematics and Statistics - Research Publications

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A converse to Dye's theorem

Hjorth, G (AMER MATHEMATICAL SOC, 2005)

Every non-amenable countable group induces orbit inequivalent ergodic equivalence relations on standard Borel probability spaces. Not every free, ergodic, measure preserving action of F 2 \mathbb {F}_2 on a standard Borel probability space is orbit equivalent to an action of a countable group on an inverse limit of finite spaces. There is a treeable non-hyperfinite Borel equivalence relation which is not universal for treeable in the ≤ B \leq _B ordering.
The classification problem for p-local torsion-free abelian groups of rank two

Hjorth, G ; Thomas, S (WORLD SCIENTIFIC PUBL CO PTE LTD, 2006-12)

We prove that if p ≠ q are distinct primes, then the classification problems for p-local and q-local torsion-free abelian groups of rank two are incomparable with respect to Borel reducibility.
Rigidity theorems for actions of product groups and countable Borel equivalence relations

HJORTH, G ; Kechris, AS ( 2005)