Measure reducibility of countable Borel equivalence relations
Logic
2020-02-25 v1 Dynamical Systems
Abstract
We show that every basis for the countable Borel equivalence relations strictly above under measure reducibility is uncountable, thereby ruling out natural generalizations of the Glimm-Effros dichotomy. We also push many known results concerning the abstract structure of the measure reducibility hierarchy to its base, using arguments substantially simpler than those previously employed.
Cite
@article{arxiv.2002.09655,
title = {Measure reducibility of countable Borel equivalence relations},
author = {Clinton T. Conley and Benjamin D. Miller},
journal= {arXiv preprint arXiv:2002.09655},
year = {2020}
}