Talk:Borel equivalence relation

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Geometry guy 18:43, 21 May 2007 (UTC)

Planned expansion of this article:

Hierarchy of Borel cardinalities
- Finite cardinals, , , E₀
  - Dichotomies: No cardinals between $\mathbb{N}$ and $\mathbb{R}$ (Silver-Harrington). No cardinals between $\mathbb{R}$ and $E 0$ (Harrington-Kechris-Louveau, generalization of Glimm-Effros).
- After that, no longer a linear order
  - But there's another local dichotomy between $E 0$ 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.

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