The Borel complexity of von Neumann equivalence
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The Borel complexity of von Neumann equivalence. / Moroz, Inessa; Törnquist, Asger.
I: Annals of Pure and Applied Logic, Bind 172, Nr. 5, 102913, 2021.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - The Borel complexity of von Neumann equivalence
AU - Moroz, Inessa
AU - Törnquist, Asger
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Ergodic theory
KW - Global theory of measure preserving actions
KW - Group measure space factors
UR - http://www.scopus.com/inward/record.url?scp=85095856209&partnerID=8YFLogxK
U2 - 10.1016/j.apal.2020.102913
DO - 10.1016/j.apal.2020.102913
M3 - Journal article
AN - SCOPUS:85095856209
VL - 172
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
SN - 0168-0072
IS - 5
M1 - 102913
ER -
ID: 257977197