A generic-classification dichotomy for analytic equivalence relations

Let EE be an analytic equivalence relation. A turbulent equivalence relation is an equivalence relation satisfying the generalized notion of turbulence introduced in the source.

Generic-classification dichotomy. Exactly one of the following holds:

  1. A turbulent equivalence relation is Borel reducible to EE.
  2. EE admits a generically absolute classification.

This is proposed as an extension of Hjorth's turbulence dichotomy from classification by countable structures to generic classification for non-orbit equivalence relations. Its status is unresolved in the source.

Sources & referencesView supporting material

Primary source

Assaf Shani, “Classifying invariants for E_1: A tail of a generic real”, arXiv:2112.12881 (2021).

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