{"id":"https://openalex.org/W1592339824","doi":"https://doi.org/10.48550/arxiv.1310.5138","title":"Existentially closed II_1 factors","display_name":"Existentially closed II_1 factors","publication_year":2013,"publication_date":"2013-10-18","ids":{"openalex":"https://openalex.org/W1592339824","doi":"https://doi.org/10.48550/arxiv.1310.5138","mag":"1592339824"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1310.5138","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1310.5138","pdf_url":"https://arxiv.org/pdf/1310.5138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1310.5138","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073593778","display_name":"Ilijas Farah","orcid":"https://orcid.org/0000-0001-7703-6931","observed_orcids":["https://orcid.org/0000-0001-7703-6931"]},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Farah, Ilijas","raw_affiliation_strings":["Department of Mathematics and Statistics , York University , 4700 Keele Street , North York , Ontario , Canada,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics , York University , 4700 Keele Street , North York , Ontario , Canada,","institution_ids":["https://openalex.org/I192455969"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064180225","display_name":"Isaac Goldbring","orcid":"https://orcid.org/0000-0003-0341-0251","observed_orcids":["https://orcid.org/0000-0003-0341-0251"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Goldbring, Isaac","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021510208","display_name":"Bradd Hart","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hart, Bradd","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Sherman, David","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Sherman, David","raw_affiliation_strings":["Department of Mathematical Sci- ences , University of Copenhagen , Universitetsparken 5 , 2100 Copenhagen , Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sci- ences , University of Copenhagen , Universitetsparken 5 , 2100 Copenhagen , Denmark","institution_ids":["https://openalex.org/I124055696"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9272000193595886,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9272000193595886,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.06589999794960022,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.0013000000035390258,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ii-1-factors","display_name":"II_1 factors","score":0.968999981880188},{"id":"https://openalex.org/keywords/model-completeness","display_name":"model completeness","score":0.7160000205039978},{"id":"https://openalex.org/keywords/forcing","display_name":"forcing","score":0.46799999475479126},{"id":"https://openalex.org/keywords/von-neumann-algebras","display_name":"von Neumann algebras","score":0.7059999704360962}],"concepts":[{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6295455694198608},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5792490839958191},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.5612375736236572},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.42055124044418335},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3835200071334839},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37666767835617065},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15366658568382263},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06313589215278625},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:arXiv.org:1310.5138","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1310.5138","pdf_url":"https://arxiv.org/pdf/1310.5138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:1592339824","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1310.5138","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.699.6787","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.699.6787","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.yorku.ca/%7Eifarah/Ftp/ec.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.742.2614","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.742.2614","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1310.5138.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1310.5138","doi":"https://doi.org/10.48550/arxiv.1310.5138","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1310.5138","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1310.5138","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1310.5138","pdf_url":"https://arxiv.org/pdf/1310.5138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.5699999928474426,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"study_designs":[],"awards":[{"id":"https://openalex.org/G1389399587","display_name":"Probabilistic Techniques in Mathematical Phylogenetics","funder_award_id":"1007144","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4107545739","display_name":"Operator algebras and model theory","funder_award_id":"1201454","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6095089026","display_name":null,"funder_award_id":"10-082689/FNU","funder_id":"https://openalex.org/F4320322928","funder_display_name":"Danmarks Frie Forskningsfond"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322928","display_name":"Danmarks Frie Forskningsfond","ror":"https://ror.org/02sptwz63"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1488454741","https://openalex.org/W1542113445","https://openalex.org/W1552483124","https://openalex.org/W1571457417","https://openalex.org/W1983046429","https://openalex.org/W2040471596","https://openalex.org/W2060951741","https://openalex.org/W2171661581","https://openalex.org/W2499459198","https://openalex.org/W2593235688"],"related_works":["https://openalex.org/W2762291046","https://openalex.org/W3194035235","https://openalex.org/W2171661581","https://openalex.org/W2167217619","https://openalex.org/W3105334584","https://openalex.org/W1676463131","https://openalex.org/W3105725044","https://openalex.org/W3127408556","https://openalex.org/W3113853335","https://openalex.org/W2030973323","https://openalex.org/W2167651941","https://openalex.org/W2256172368","https://openalex.org/W2319305328","https://openalex.org/W2164200085","https://openalex.org/W2010971114","https://openalex.org/W2001752461","https://openalex.org/W1530861922","https://openalex.org/W2883406053","https://openalex.org/W1650490357","https://openalex.org/W1994483064"],"abstract_inverted_index":{"We":[0,36],"examine":[1],"the":[2,14,51],"properties":[3],"of":[4,19,65],"existentially":[5,21,62],"closed":[6,22,63],"(R^omega-embeddable)":[7,23],"II_1":[8,24],"factors.":[9],"In":[10],"particular,":[11],"we":[12],"use":[13,50],"fact":[15],"that":[16,31,39,56],"every":[17],"automorphism":[18],"an":[20],"factor":[25],"is":[26,33,41],"approximately":[27],"inner":[28],"to":[29,54],"prove":[30,55],"Th(R)":[32,40],"not":[34],"model-complete.":[35],"also":[37],"show":[38],"complete":[42],"for":[43],"both":[44],"finite":[45],"and":[46,49],"infinite":[47],"forcing":[48],"latter":[52],"result":[53],"there":[57],"exist":[58],"continuum":[59],"many":[60],"nonisomorphic":[61],"models":[64],"Th(R).":[66]},"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}