Dichotomy Theorems for Families of Non-Cofinal Essential Complexity

John D. Clemens, Dominique Lecomte, Benjamin D. Miller

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 E∈F or F is Borel reducible to E, then F consists solely of smooth equivalence relations, thus the dichotomy is equivalent to a known theorem.

Original languageAmerican English
Pages (from-to)285-299
Number of pages15
JournalAdvances in Mathematics
Volume304
DOIs
StatePublished - 2 Jan 2017

Keywords

  • Complexity
  • Dichotomy
  • Equivalence relation
  • Smooth

EGS Disciplines

  • Mathematics

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