Talk:Borel equivalence relation

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Mathematics rating: Stub Class Mid Priority  Field: Foundations, logic, and set theory

Planned expansion of this article:

  • Hierarchy of Borel cardinalities
    • Finite cardinals, \mathbb{N}, \mathbb{R}, E0
      • Dichotomies: No cardinals between \mathbb{N} and \mathbb{R} (Silver-Harrington). No cardinals between \mathbb{R} and E0 (Harrington-Kechris-Louveau, generalization of Glimm-Effros).
    • After that, no longer a linear order
      • But there's another local dichotomy between E0 and \ell^1 (Hjorth) (Well, almost.)
    • Countable equivalence relations
    • Equivalence relations induced by Polish group actions
      • Equivalence relations reducible to isomorphism on countable structures
      • Turbulent actions
      • Louveau-Velickovic relations
  • Hyperfinite equivalence relations and the union problem.