Asger Tornquist
Orbit Equivalence and F_n.
Wed, 12/09/2009 - 16:01 — SomNambulAuthors: Asger Tornquist
Subjects: Group Theory
AbstractIn this paper we show that there are ``E_0 many'' orbit inequivalent free
actions of the free groups F_n, $2\leq n\leq\infty$, by measure preserving
transformations on a standard Borel probability space. In particular, there are
uncountably many such actions.Turbulence and Araki-Woods factors.
Wed, 12/09/2009 - 16:01 — SomNambulAuthors: Asger Tornquist, Roman Sasyk
Subjects: Operator Algebras
AbstractUsing Baire category techniques we prove that Araki-Woods factors are not
classifiable by countable structures. As a result, we obtain a strengthening
and a new proof of the well-known theorem of Woods that the isomorphism problem
for ITPFI factors is not smooth, as well as a new and more direct proof that
the isomorphism relation for injective type III_0 factors is not classifiable
by countable structures.On the pointwise implementation of near-actions.
Wed, 09/23/2009 - 13:19 — SomNambulAuthors: Asger Tornquist
Subjects: Logic
AbstractWe show that the continuum hypothesis implies that every measure preserving
near-action of a group on a standard Borel probability $(X,\mu)$ has a
pointwise implementation by Borel measure preserving automorphisms.On the pointwise implementation of near-actions.
Wed, 09/23/2009 - 13:19 — SomNambulAuthors: Asger Tornquist
Subjects: Logic
AbstractWe show that the continuum hypothesis implies that every measure preserving
near-action of a group on a standard Borel probability $(X,\mu)$ has a
pointwise implementation by Borel measure preserving automorphisms.A co-analytic maximal set of orthogonal measures.
Thu, 08/27/2009 - 13:23 — SomNambulAuthors: Vera Fischer, Asger Tornquist
Subjects: Logic
AbstractWe prove that if $V=L$ then there is a $\Pi^1_1$ maximal orthogonal (i.e.
mutually singular) set of measures on Cantor space. This provides a natural
counterpoint to the well-known Theorem of Preiss and Rataj that no analytic set
of measures can be maximal orthogonal.A co-analytic maximal set of orthogonal measures.
Thu, 08/27/2009 - 13:23 — SomNambulAuthors: Vera Fischer, Asger Tornquist
Subjects: Logic
AbstractWe prove that if $V=L$ then there is a $\Pi^1_1$ maximal orthogonal (i.e.
mutually singular) set of measures on Cantor space. This provides a natural
counterpoint to the well-known Theorem of Preiss and Rataj that no analytic set
of measures can be maximal orthogonal.
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