5 papers
A co-analytic maximal set of orthogonal measures
Vera Fischer, Asger Tornquist
We prove that if then there is a maximal orthogonal (i.e. mutually singular) set of measures on Cantor space. This provides a natural counterpoint to the well-known T…
The Effective Theory of Borel Equivalence Relations
Ekaterina B. Fokina, Sy-David Friedman, Asger Tornquist
The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver and Harrington-Kechris-L…
The classification problem for von Neumann factors
Roman Sasyk, Asger Tornquist
We prove that it is not possible to classify separable von Neumann factors of types $\II_1$, $\II_\infty$ or $\III_λ$, , up to isomorphism by a Borel measurable assig…
Definable Davies' Theorem
Asger Tornquist, William Weiss
We prove the following analogue of a Theorem of R.O. Davies: Every function can be represented as a sum of rectangular functions if and only if…
Localized cohomology and some applications of Popa's cocycle super-rigidity theorem
Asger Tornquist
We prove that orbit equivalence of measure preserving ergodic a.e. free actions of a countable group with the relative property (T) is a complete analytic equivalence relation.