An anti-classification theorem for ergodic measure preserving transformations

Foreman, Matthew, and Weiss, Benjamin. "An anti-classification theorem for ergodic measure preserving transformations." Journal of the European Mathematical Society 006.3 (2004): 277-292. <http://eudml.org/doc/277273>.

@article{Foreman2004,
abstract = {Despite many notable advances the general problem of classifying ergodic measure preserving transformations (MPT) has remained wide open. We show that the action of the whole group of MPT’s on ergodic actions by conjugation is turbulent in the sense of G. Hjorth. The type of classifications ruled out by this property include countable algebraic objects such as those that occur in the Halmos–von Neumann theorem classifying ergodic MPT’s with pure point spectrum. We treat both the classical case of $\mathbb \{$\}Z as well as the case of general countable amenable groups.},
author = {Foreman, Matthew, Weiss, Benjamin},
journal = {Journal of the European Mathematical Society},
keywords = {measure preserving transformations; amenable groups; anti-classification; entropy; isomorphism; anti-classification; entropy; isomorphism},
language = {eng},
number = {3},
pages = {277-292},
publisher = {European Mathematical Society Publishing House},
title = {An anti-classification theorem for ergodic measure preserving transformations},
url = {http://eudml.org/doc/277273},
volume = {006},
year = {2004},
}

TY - JOUR
AU - Foreman, Matthew
AU - Weiss, Benjamin
TI - An anti-classification theorem for ergodic measure preserving transformations
JO - Journal of the European Mathematical Society
PY - 2004
PB - European Mathematical Society Publishing House
VL - 006
IS - 3
SP - 277
EP - 292
AB - Despite many notable advances the general problem of classifying ergodic measure preserving transformations (MPT) has remained wide open. We show that the action of the whole group of MPT’s on ergodic actions by conjugation is turbulent in the sense of G. Hjorth. The type of classifications ruled out by this property include countable algebraic objects such as those that occur in the Halmos–von Neumann theorem classifying ergodic MPT’s with pure point spectrum. We treat both the classical case of $\mathbb {$}Z as well as the case of general countable amenable groups.
LA - eng
KW - measure preserving transformations; amenable groups; anti-classification; entropy; isomorphism; anti-classification; entropy; isomorphism
UR - http://eudml.org/doc/277273
ER -