Online research in philosophy

We announce some new results regarding the classification problem for separable von Neumann algebras. Our results are obtained by applying the notion of Borel reducibility and Hjorth's theory of turbulence to the isomorphism relation for separable von Neumann algebras.

In this paper we show that there are "E₀ many" orbit inequivalent free actions of the free groups Fn. 2 ≤ n ≤ ∞ by measure preserving transformations on a standard Borel probability space. In particular, there are uncountably many such actions.