# Talk:Borel equivalence relation

WikiProject Mathematics (Rated Stub-class, Mid-importance)
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Mathematics rating:
 Stub Class
 Mid Importance
Field: Foundations, logic, and set theory

• Finite cardinals, $\mathbb{N}$, $\mathbb{R}$, $E_0$
• 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).
• But there's another local dichotomy between $E_0$ and $\ell^1$ (Hjorth) (Well, almost.)