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1
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Mixing actions of groups with the Haagerup approximation property

100%
Hjorth G.
Fundamenta Mathematicae
|
2009
|
tom 203
|
nr 1
47-56
EN
A countable group Γ has the Haagerup approximation property if and only if the mixing actions are dense in the space of all actions of Γ.
2
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The isomorphism relation on countable torsion free abelian groups

100%
Hjorth G.
Fundamenta Mathematicae
|
2002
|
tom 175
|
nr 3
241-257
EN
The isomorphism relation on countable torsion free abelian groups is non-Borel.
3
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Recent developments in the theory of Borel reducibility

63%
Hjorth G., Kechris A.
Fundamenta Mathematicae
|
2001
|
tom 170
|
nr 1-2
21-52
EN
Let E₀ be the Vitali equivalence relation and E₃ the product of countably many copies of E₀. Two new dichotomy theorems for Borel equivalence relations are proved. First, for any Borel equivalence relation E that is (Borel) reducible to E₃, either E is reducible to E₀ or else E₃ is reducible to E. Second, if E is a Borel equivalence relation induced by a Borel action of a closed subgroup of the infinite symmetric group that admits an invariant metric, then either E is reducible to a countable Borel equivalence relation or else E₃ is reducible to E. We also survey a number of results and conjectures concerning the global structure of reducibility on Borel equivalence relations.
4
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Conjugacy equivalence relation on subgroups

51%
Andretta A., Camerlo R., Hjorth G.
Fundamenta Mathematicae
|
2001
|
tom 167
|
nr 3
189-212
EN
If G is a countable group containing a copy of F₂ then the conjugacy equivalence relation on subgroups of G attains the maximal possible complexity.
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