{"id":"https://openalex.org/W3014239444","doi":"https://doi.org/10.1093/logcom/exaa059","title":"Operator algebras with hyperarithmetic theory","display_name":"Operator algebras with hyperarithmetic theory","publication_year":2020,"publication_date":"2020-09-06","ids":{"openalex":"https://openalex.org/W3014239444","doi":"https://doi.org/10.1093/logcom/exaa059","mag":"3014239444"},"language":"en","primary_location":{"id":"doi:10.1093/logcom/exaa059","is_oa":true,"landing_page_url":"https://doi.org/10.1093/logcom/exaa059","pdf_url":"https://academic.oup.com/logcom/article-pdf/31/2/612/36430734/exaa059.pdf","source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://academic.oup.com/logcom/article-pdf/31/2/612/36430734/exaa059.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064180225","display_name":"Isaac Goldbring","orcid":"https://orcid.org/0000-0003-0341-0251"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Isaac Goldbring","raw_affiliation_strings":["Department of Mathematics, University of California, Irvine, 340 Rowland Hall (Bldg.# 400), Irvine, CA 92697, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Irvine, 340 Rowland Hall (Bldg.# 400), Irvine, CA 92697, USA","institution_ids":["https://openalex.org/I204250578"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021510208","display_name":"Bradd Hart","orcid":null},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Bradd Hart","raw_affiliation_strings":["Department of Mathematics and Statistics, McMaster University, 1280 Main St., Hamilton, Ontario L8S 4L8, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, McMaster University, 1280 Main St., Hamilton, Ontario L8S 4L8, Canada","institution_ids":["https://openalex.org/I98251732"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064180225"],"corresponding_institution_ids":["https://openalex.org/I204250578"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":{"value":4151,"currency":"USD","value_usd":4151},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12711087,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"2","first_page":"612","last_page":"629"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9970999956130981,"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":0.9970999956130981,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9624999761581421,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.957099974155426,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.6872478127479553},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6529062986373901},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6303425431251526},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5449175238609314},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4859298765659332},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4754640460014343},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.45822298526763916},{"id":"https://openalex.org/keywords/operator-algebra","display_name":"Operator algebra","score":0.45708465576171875},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.44907763600349426},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4299023747444153},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3916158676147461},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38007989525794983},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3671969175338745},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1531868278980255},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.059909313917160034},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.058258056640625},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04534804821014404}],"concepts":[{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.6872478127479553},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6529062986373901},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6303425431251526},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5449175238609314},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4859298765659332},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4754640460014343},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.45822298526763916},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.45708465576171875},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.44907763600349426},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4299023747444153},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3916158676147461},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38007989525794983},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3671969175338745},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1531868278980255},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.059909313917160034},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.058258056640625},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04534804821014404},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1093/logcom/exaa059","is_oa":true,"landing_page_url":"https://doi.org/10.1093/logcom/exaa059","pdf_url":"https://academic.oup.com/logcom/article-pdf/31/2/612/36430734/exaa059.pdf","source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2004.02299","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.02299","pdf_url":"https://arxiv.org/pdf/2004.02299","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},{"id":"mag:3014239444","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2004.02299.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"doi:10.48550/arxiv.2004.02299","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2004.02299","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"article"}],"best_oa_location":{"id":"doi:10.1093/logcom/exaa059","is_oa":true,"landing_page_url":"https://doi.org/10.1093/logcom/exaa059","pdf_url":"https://academic.oup.com/logcom/article-pdf/31/2/612/36430734/exaa059.pdf","source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8005843364","display_name":null,"funder_award_id":"1349399","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3014239444.pdf","grobid_xml":"https://content.openalex.org/works/W3014239444.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1484200610","https://openalex.org/W1542113445","https://openalex.org/W1971225516","https://openalex.org/W1975830167","https://openalex.org/W2045356657","https://openalex.org/W2068855023","https://openalex.org/W2167217619","https://openalex.org/W2171661581","https://openalex.org/W2280978717","https://openalex.org/W2468512922","https://openalex.org/W2724657093","https://openalex.org/W2963023910","https://openalex.org/W2963166739","https://openalex.org/W2963768093","https://openalex.org/W6631200304","https://openalex.org/W6635383452","https://openalex.org/W6729439240","https://openalex.org/W6747536849","https://openalex.org/W6779342127"],"related_works":["https://openalex.org/W3088572834","https://openalex.org/W2948001466","https://openalex.org/W1994002430","https://openalex.org/W3111942646","https://openalex.org/W2971953768","https://openalex.org/W2002211781","https://openalex.org/W2414377137","https://openalex.org/W2001091064","https://openalex.org/W2000397990","https://openalex.org/W2950157900","https://openalex.org/W2059893861","https://openalex.org/W3123751261","https://openalex.org/W1983306381","https://openalex.org/W2963111665","https://openalex.org/W3159486807","https://openalex.org/W3103548895","https://openalex.org/W2949935769","https://openalex.org/W3015643064","https://openalex.org/W2000984834","https://openalex.org/W1977812351"],"abstract_inverted_index":{"Abstract":[0],"We":[1,64],"show":[2,66],"that":[3,67,78,89,101],"the":[4,11,62,68,79],"following":[5],"operator":[6],"algebras":[7],"have":[8,83,104],"hyperarithmetic":[9,75,105],"theory:":[10],"hyperfinite":[12],"II$_1$":[13,97,115],"factor":[14,98],"$\\mathcal":[15,71],"R$,":[16],"$L(\\varGamma":[17],")$":[18,31,41,54],"for":[19,32,42],"$\\varGamma":[20,33,43],"$":[21,34,44],"a":[22,35,45,74],"finitely":[23,36,46],"generated":[24,47],"group":[25,48],"with":[26,49],"solvable":[27,50],"word":[28,51],"problem,":[29,52],"$C^*(\\varGamma":[30],"presented":[37],"group,":[38],"$C^*_\\lambda":[39],"(\\varGamma":[40],"$C(2^\\omega":[53],"and":[55],"$C(\\mathbb":[56],"P)$":[57],"(where":[58],"$\\mathbb":[59],"P$":[60],"is":[61,92],"pseudoarc).":[63],"also":[65],"Cuntz":[69],"algebra":[70],"O_2$":[72],"has":[73],"theory":[76],"provided":[77],"Kirchberg":[80],"embedding":[81],"problems":[82],"affirmative":[84],"answers.":[85],"Finally,":[86],"we":[87],"prove":[88],"if":[90],"there":[91,108],"an":[93],"existentially":[94],"closed":[95],"(e.c.)":[96],"(resp.":[99,117],"$\\textrm{C}^*$-algebra)":[100],"does":[102],"not":[103],"theory,":[106],"then":[107],"are":[109],"continuum":[110],"many":[111],"theories":[112],"of":[113],"e.c.":[114,118],"factors":[116],"$\\textrm{C}^*$-algebras).":[119]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
