Measure reducibility of countable Borel equivalence relations

Clinton T. Conley; Benjamin D. Miller

doi:10.4007/annals.2017.185.2.1

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arXiv · 2002.09655

Measure reducibility of countable Borel equivalence relations

Clinton T. Conley·Benjamin D. Miller

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Abstract

We show that every basis for the countable Borel equivalence relations strictly above $\mathbb{E}_0$ 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.

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BibTeX RIS

Clinton T. Conley, Benjamin D. Miller. 2020-02-22. Measure reducibility of countable Borel equivalence relations. https://doi.org/10.4007/annals.2017.185.2.1

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