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The Borel complexity of von Neumann equivalence
Annals of Pure and Applied Logic ( IF 0.6 ) Pub Date : 2020-10-13 , DOI: 10.1016/j.apal.2020.102913
Inessa Moroz , Asger Törnquist

We prove that for a countable discrete group Γ containing a copy of the free group Fn, for some 2n, as a normal subgroup, the equivalence relations of conjugacy, orbit equivalence and von Neumann equivalence of the ergodic a.e. free probability measure preserving actions of Γ are analytic non-Borel equivalence relations in the Polish space of probability measure preserving Γ-actions. As a consequence we obtain that the isomorphism relation in the spaces of separably acting factors of type II1, II and IIIλ, 0λ1, are analytic and not Borel when these spaces are given the Effros Borel structure.



中文翻译:

冯·诺依曼等价的Borel复杂度

我们证明对于包含自由组副本的可数离散组Γ Fñ, 对于一些 2ñ作为正常子群,Γ遍历ae无概率测度保持作用的共轭,轨道等价关系和von Neumann等价关系是波兰的概率测度保持Γ作用空间中的解析非Borel等价关系。结果,我们得到在类型分别起作用的因子的空间中的同构关系II1个II三级λ0λ1个当给这些空间赋予Effros Borel结构时,是而不是Borel。

更新日期:2020-10-13
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