2 problems

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Weiss's hyperfiniteness conjecture for countable amenable group actions
Weiss's conjecture. Every orbit equivalence relation induced by a Borel action of a countable amenable group is hyperfinite.
Conjectureopenamenable-groups descriptive-set-theory orbit-equivalence-relationsarXiv posted 2 days ago
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Topological Vaught Conjecture for Polish group actions
Topological Vaught Conjecture. For every Polish $G$ -space $(\mathcal{X},G,\cdot)$ , the orbit equivalence relation $E_G$ has either countably many or perfectly many classes.
Conjectureopendescriptive-set-theory orbit-equivalence-relations polish-groupsarXiv posted 2 days ago

Weiss's hyperfiniteness conjecture for countable amenable group actions