16 research outputs found
Turbulence and Araki-Woods factors
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.Comment: 16 page
Definable Davies' Theorem
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 all reals are constructible.Comment: Final version, to appear in Fundamenta Mathematica
Projective maximal families of orthogonal measures with large continuum
We study maximal orthogonal families of Borel probability measures on
(abbreviated m.o. families) and show that there are generic
extensions of the constructible universe in which each of the following
holds:
(1) There is a -definable well order of the reals, there is a
-definable m.o. family, there are no -definable
m.o. families and (in fact any reasonable
value of will do).
(2) There is a -definable well order of the reals, there is a
-definable m.o. family, there are no -definable
m.o. families, and .Comment: 12 page