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As a consequence we obtain that the isomorphism relation in the spaces of separably acting factors of type $\\II_1$, $\\II_\\infty$ and $\\III_\\lambda$, $0\\leq\\lambda\\leq 1$, are analytic and not Borel when"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1109.2351","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-11T20:34:21Z","cross_cats_sorted":["math.GR","math.LO","math.OA"],"title_canon_sha256":"719937b02b3149367a777b905370ecb75f7a79cc4f5311a3dc80a334e896834e","abstract_canon_sha256":"072fe94efa8883183bf74323ec2b1186dc3c6c72019dff7e527399a777095500"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:14.136351Z","signature_b64":"Qxt6eZwOLz6HUFgIOHo2QkLMCMeEQQL1swEXInakwp/k2T82m0RO6oFBcES8Ncep7JNV5uAYDEbwd52MlvlPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fd9c85106d9b7874aa971aa61897ca982e5620d5dabd6fa169bed288655e6bf","last_reissued_at":"2026-05-18T03:55:14.135844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:14.135844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Borel complexity of von Neumann equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.LO","math.OA"],"primary_cat":"math.DS","authors_text":"Asger Tornquist, Inessa Epstein","submitted_at":"2011-09-11T20:34:21Z","abstract_excerpt":"We prove that for a countable discrete group $\\Gamma$ containing a copy of the free group $\\F_n$, for some $2\\leq n\\leq\\infty$, as a normal subgroup, the equivalence relations of conjugacy, orbit equivalence and von Neumann equivalence of the ergodic a.e. free actions of $\\Gamma$ are analytic non-Borel equivalence relations in the Polish space of probability measure preserving $\\Gamma$ actions. 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