{"id":"https://openalex.org/W1972220550","doi":"https://doi.org/10.2307/2275278","title":"The Beth-closure of <i>\u2112</i>(<i>Q<sub>\u03b1</sub></i>) is not finitely generated","display_name":"The Beth-closure of <i>\u2112</i>(<i>Q<sub>\u03b1</sub></i>) is not finitely generated","publication_year":1992,"publication_date":"1992-06-01","ids":{"openalex":"https://openalex.org/W1972220550","doi":"https://doi.org/10.2307/2275278","mag":"1972220550"},"language":"en","primary_location":{"id":"doi:10.2307/2275278","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275278","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078573449","display_name":"Lauri Hella","orcid":"https://orcid.org/0000-0002-9117-8124"},"institutions":[{"id":"https://openalex.org/I2800229700","display_name":"Helsinki Institute of Physics","ror":"https://ror.org/01x2x1522","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I2800229700","https://openalex.org/I63548447","https://openalex.org/I94722563","https://openalex.org/I9927081"]},{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Lauri Hella","raw_affiliation_strings":["Department of Mathematics, University of Helsinki, 00100 Helsinki, Finland, E-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Helsinki, 00100 Helsinki, Finland, E-mail:","institution_ids":["https://openalex.org/I133731052","https://openalex.org/I2800229700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031424171","display_name":"Kerkko Luosto","orcid":"https://orcid.org/0009-0007-3911-766X"},"institutions":[{"id":"https://openalex.org/I32943570","display_name":"Helsinki Institute for Information Technology","ror":"https://ror.org/05kph4940","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I32943570","https://openalex.org/I9927081"]},{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]},{"id":"https://openalex.org/I2800229700","display_name":"Helsinki Institute of Physics","ror":"https://ror.org/01x2x1522","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I2800229700","https://openalex.org/I63548447","https://openalex.org/I94722563","https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Kerkko Luosto","raw_affiliation_strings":["Department of Mathematics, University of Helsinki, 00100 Helsinki, Finland, E-maii:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Helsinki, 00100 Helsinki, Finland, E-maii:","institution_ids":["https://openalex.org/I32943570","https://openalex.org/I2800229700","https://openalex.org/I133731052"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078573449"],"corresponding_institution_ids":["https://openalex.org/I133731052","https://openalex.org/I2800229700"],"apc_list":null,"apc_paid":null,"fwci":0.4644,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58249875,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"57","issue":"2","first_page":"442","last_page":"448"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9757000207901001,"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"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9625999927520752,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uncountable-set","display_name":"Uncountable set","score":0.9255738258361816},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.866019070148468},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6665480732917786},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6187934875488281},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.6073245406150818},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.515275239944458},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49816131591796875},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4721275269985199},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3378404974937439},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17129391431808472},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.06750237941741943},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.042728573083877563}],"concepts":[{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.9255738258361816},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.866019070148468},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6665480732917786},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6187934875488281},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.6073245406150818},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.515275239944458},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49816131591796875},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4721275269985199},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3378404974937439},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17129391431808472},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.06750237941741943},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.042728573083877563},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2275278","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275278","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W251225716","https://openalex.org/W1965302155","https://openalex.org/W2044340169","https://openalex.org/W2065676868","https://openalex.org/W2076662767","https://openalex.org/W6641276971"],"related_works":["https://openalex.org/W2100222222","https://openalex.org/W1982069151","https://openalex.org/W2256572025","https://openalex.org/W4303646992","https://openalex.org/W2952146172","https://openalex.org/W4300882518","https://openalex.org/W2018852434","https://openalex.org/W196788981","https://openalex.org/W24519920","https://openalex.org/W2185713319"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"prove":[2],"that":[3,76],"if":[4],"\u2135":[5],"\u03b1":[6,19,52,83],"is":[7,21,35,54],"uncountable":[8],"and":[9],"regular,":[10],"then":[11],"the":[12,36],"Beth-closure":[13],"of":[14,25,38,58,72],"\u2112":[15,26,48,79,86],"\u03c9\u03c9":[16,49,80,87],"(":[17,28,47,50,78,81,88],"Q":[18,29,33,51,71,82,89],")":[20],"not":[22,55,66],"a":[23,56,68],"sublogic":[24,57],"\u03b1\u03c9":[27],"n":[30,34,40],"),":[31],"where":[32],"class":[37],"all":[39],"-ary":[41],"generalized":[42],"quantifiers.":[43],"In":[44],"particular,":[45],"B":[46,77],"))":[53,84],"any":[59],"finitely":[60],"generated":[61],"logic;":[62],"i.e.,":[63],"there":[64],"does":[65],"exist":[67],"finite":[69],"set":[70],"Lindstr\u00f6m":[73],"quantifiers":[74],"such":[75],"\u2264":[85],").":[90]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}