{"id":"https://openalex.org/W1990022946","doi":"https://doi.org/10.1002/malq.200710023","title":"A constructive version of Birkhoff's theorem","display_name":"A constructive version of Birkhoff's theorem","publication_year":2008,"publication_date":"2008-01-30","ids":{"openalex":"https://openalex.org/W1990022946","doi":"https://doi.org/10.1002/malq.200710023","mag":"1990022946"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200710023","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200710023","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5054027589","display_name":"Jesper Carlstr\u00f6m","orcid":null},"institutions":[{"id":"https://openalex.org/I161593684","display_name":"Stockholm University","ror":"https://ror.org/05f0yaq80","country_code":"SE","type":"education","lineage":["https://openalex.org/I161593684"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Jesper Carlstr\u00f6m","raw_affiliation_strings":["Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden","Department of Mathematics Stockholm University SE-106 91 Stockholm Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden","institution_ids":["https://openalex.org/I161593684"]},{"raw_affiliation_string":"Department of Mathematics Stockholm University SE-106 91 Stockholm Sweden","institution_ids":["https://openalex.org/I161593684"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054027589"],"corresponding_institution_ids":["https://openalex.org/I161593684"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07079049,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"54","issue":"1","first_page":"27","last_page":"34"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.991599977016449,"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":0.991599977016449,"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/predicative-expression","display_name":"Predicative expression","score":0.9316356182098389},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8378331065177917},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.7961346507072449},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.7788589596748352},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5369256734848022},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4711042046546936},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.4497308135032654},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.44609785079956055},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4361097812652588},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40143275260925293},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.0638052225112915},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06375616788864136}],"concepts":[{"id":"https://openalex.org/C129131279","wikidata":"https://www.wikidata.org/wiki/Q1931259","display_name":"Predicative expression","level":2,"score":0.9316356182098389},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8378331065177917},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.7961346507072449},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.7788589596748352},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5369256734848022},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4711042046546936},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.4497308135032654},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.44609785079956055},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4361097812652588},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40143275260925293},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0638052225112915},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06375616788864136},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.200710023","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200710023","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W104853290","https://openalex.org/W1565484361","https://openalex.org/W2023648368","https://openalex.org/W2049352524","https://openalex.org/W2067914884","https://openalex.org/W3127823229","https://openalex.org/W4213165878","https://openalex.org/W4293176479"],"related_works":["https://openalex.org/W2954167023","https://openalex.org/W4250578329","https://openalex.org/W2064351239","https://openalex.org/W2949665548","https://openalex.org/W2114983089","https://openalex.org/W2950188642","https://openalex.org/W2028676759","https://openalex.org/W1589204344","https://openalex.org/W2257471395","https://openalex.org/W1780530600"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"version":[2,13],"of":[3,43,55,64],"Birkhoff's":[4],"theorem":[5],"is":[6,28,36,50,59,70],"proved":[7],"by":[8],"constructive,":[9],"predicative,":[10],"methods.":[11],"The":[12],"we":[14],"prove":[15],"has":[16],"two":[17],"conditions":[18],"more":[19],"than":[20],"the":[21,25,65,68],"classical":[22],"one.":[23],"First,":[24],"class":[26,69],"considered":[27],"assumed":[29,71],"to":[30,38,72],"contain":[31],"a":[32,40],"generic":[33],"family,":[34,57],"which":[35],"defined":[37],"be":[39,73],"set\u2010indexed":[41],"family":[42],"algebras":[44],"such":[45],"that":[46],"if":[47],"an":[48],"identity":[49],"valid":[51,60],"in":[52,61],"every":[53,62],"algebra":[54,63],"this":[56],"it":[58],"class.":[66],"Secondly,":[67],"closed":[74],"under":[75],"inductive":[76],"limits.":[77],"(\u00a9":[78],"2008":[79],"WILEY\u2010VCH":[80],"Verlag":[81],"GmbH":[82],"&amp;":[83],"Co.":[84],"KGaA,":[85],"Weinheim)":[86]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
