Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424906 | Advances in Mathematics | 2017 | 15 Pages |
Abstract
We prove that for every Borel equivalence relation E, either E is Borel reducible to E0, or the family of Borel equivalence relations incompatible with E has cofinal essential complexity. It follows that if F is a Borel equivalence relation and F is a family of Borel equivalence relations of non-cofinal essential complexity which together satisfy the dichotomy that for every Borel equivalence relation E, either EâF or F is Borel reducible to E, then F consists solely of smooth equivalence relations, thus the dichotomy is equivalent to a known theorem.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
John D. Clemens, Dominique Lecomte, Benjamin D. Miller,