Turbulence and Araki-Woods factors

ROMAN SASYK, ASGER TORNQUIST

JOURNAL OF FUNCTIONAL ANALYSIS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2010 vol. 259 p. 2238 - 2252

0022-1236

Using Baire category techniques we prove that Araki–Woods factors are not classifiable by countable structures. As a result, we obtain a far reaching strengthening as well as a new proof of the well-known theorem of Woods that the isomorphism problem for ITPFI factors is not smooth. We derive as a consequence that the odometer actions of Z that preserve the measure class of a finite non-atomic product measure are not classifiable up to orbit equivalence by countable structures.