The Borel complexity of von Neumann equivalence
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We prove that for a countable discrete group Γ containing a copy of the free group Fn, for some 2≤n≤∞, 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 relations in the spaces of separably acting factors of type II1, II∞ and IIIλ, 0≤λ≤1, are analytic and not Borel when these spaces are given the Effros Borel structure.
Originalsprog | Engelsk |
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Artikelnummer | 102913 |
Tidsskrift | Annals of Pure and Applied Logic |
Vol/bind | 172 |
Udgave nummer | 5 |
Antal sider | 28 |
ISSN | 0168-0072 |
DOI | |
Status | Udgivet - 2021 |
ID: 257977197