Geodesic
Measure reducibility of countable Borel equivalence relations
Clinton T. Conley1 ; Benjamin D. Miller2
1 Carnegie Mellon University, Pittsburgh, PA
2 Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Vienna, Austria
Annals of mathematics, Tome 185 (2017) no. 2, pp. 347-402.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2017.185.2.1

Clinton T. Conley 1 ; Benjamin D. Miller 2

1 Carnegie Mellon University, Pittsburgh, PA
2 Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Vienna, Austria 
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     title = {Measure reducibility of countable {Borel} equivalence relations},
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Clinton T. Conley; Benjamin D. Miller. Measure reducibility of countable Borel equivalence relations. Annals of mathematics, Tome 185 (2017) no. 2, pp. 347-402. doi : 10.4007/annals.2017.185.2.1. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.185.2.1/

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