ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

1. Logic

1991 MS Classification: 03, 04 Sofronidis, Nikolas Efstathiou, Caltech, USA Non-classification by Countable Structures in spaces of Measures, Self-adjoint and Unitary Operators. If X is any locally compact, perfect, Polish space and P (X) denotes the Polish space of probability Borel measures on X, equipped with the w^{∗}- toplogy, while ∼ denotes measure equivalence on P (X), then ∼ does not admit classification by countable structures. In particular, for a complete manifold M, if ∼_{C^{r}} denotes C^{r}-measure equivalence on P (M), in the sense that the corresponding Radon-Nikodym derivatives are of the class C^{r} (r being a natural number or infinity), then ∼_{C^{r}} does not admit classification by countable structures. If H is any separable complex Hilbert space, while U(H) denotes the Polish group of unitary operators on H and S_{1}(H) denotes the Polish space of self-adjoint operators on H with norm at most one, both equipped with the strong operator topology, then the conjugation action of U(H) on both U(H) and S_{1}(H) is generically turbulent