The conjugacy relation on unitary representations
We show that the unitary conjugacy relation for unitary representations of a second countable locally compact group on a separable Hilbert space is a Borel equivalence relation.
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arXiv subjects
Greg Hjorth
Publications and source records attributed to Greg Hjorth.
Independently Axiomatizable L_{omega_1,omega} Theories
In partial answer to a question posed by Arnie Miller (http://www.math.wisc.edu/~miller/res/problem.pdf) and X. Caicedo, we obtain sufficient conditions for an L_{omega_1,omega} theory to have an independent axiomatization. As a consequence we obtain two corollaries: The first, assuming Vaught's Conjecture, every L_{omega_1,omega} theory in a countable language has an independent axiomatization. The second, this time outright in ZFC, every intersection of a family of Borel sets can be formed as the intersection of a family of independent Borel sets.
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Vaught's conjecture on analytic sets
This paper obtains an algebraic characterization of the Polish groups that satisfy Vaught's conjecture on $\bfΣ^1_1$ sets.
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A universal Polish G-space
If G is a Polish group, then there is a Polish G-space X which is universal among Polish G-spaces with respect to continuous G-embeddings.
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Sharper changes in topologies
Becker and Kechris showed that if a Polish group G acts continuously on a Polish space X, then for any invariant Borel set B we can change the topology on X so that B becomes open, the Borel structure is preserved, and the action continues to be continuous. In this brief paper a short proof is presented for their theorem. The method also gives optimal bounds in terms of minimizing the change to the original topology.
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The Cardinality of the second uniform indiscernible
When the second uniform indiscernible is $\aleph_{2}$, the Martin-Solovay tree only constructs countably many reals; this resolves a number of open questions in descriptive set theory.
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