{"id":"https://openalex.org/W2156724103","doi":"https://doi.org/10.2178/bsl/1182353917","title":"Computability-Theoretic Complexity of Countable Structures","display_name":"Computability-Theoretic Complexity of Countable Structures","publication_year":2002,"publication_date":"2002-12-01","ids":{"openalex":"https://openalex.org/W2156724103","doi":"https://doi.org/10.2178/bsl/1182353917","mag":"2156724103"},"language":"en","primary_location":{"id":"doi:10.2178/bsl/1182353917","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1182353917","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin 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/A5071875842","display_name":"Valentina Harizanov","orcid":"https://orcid.org/0000-0002-6626-5074"},"institutions":[{"id":"https://openalex.org/I193531525","display_name":"George Washington University","ror":"https://ror.org/00y4zzh67","country_code":"US","type":"education","lineage":["https://openalex.org/I193531525"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Valentina S. Harizanov","raw_affiliation_strings":["Department of Mathematics, The George Washington University, Washington, D.C. 20052, U.S.A.E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The George Washington University, Washington, D.C. 20052, U.S.A.E-mail:","institution_ids":["https://openalex.org/I193531525"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071875842"],"corresponding_institution_ids":["https://openalex.org/I193531525"],"apc_list":null,"apc_paid":null,"fwci":0.6921,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.71329204,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"8","issue":"4","first_page":"457","last_page":"477"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T11567","display_name":"semigroups and automata theory","score":0.9861999750137329,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9833999872207642,"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/computability-theory","display_name":"Computability theory","score":0.8278661966323853},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.7912949323654175},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.7677044868469238},{"id":"https://openalex.org/keywords/computable-analysis","display_name":"Computable analysis","score":0.7444530129432678},{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.7323679327964783},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7157277464866638},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.7084078192710876},{"id":"https://openalex.org/keywords/van-der-waerdens-theorem","display_name":"Van der Waerden's theorem","score":0.5540909171104431},{"id":"https://openalex.org/keywords/ordered-field","display_name":"Ordered field","score":0.5199743509292603},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5013217926025391},{"id":"https://openalex.org/keywords/gap-theorem","display_name":"Gap theorem","score":0.4889947175979614},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4850853979587555},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.45862358808517456},{"id":"https://openalex.org/keywords/model-theory","display_name":"Model theory","score":0.4389949440956116},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3772531747817993},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28969520330429077},{"id":"https://openalex.org/keywords/fundamental-theorem","display_name":"Fundamental theorem","score":0.1257152557373047}],"concepts":[{"id":"https://openalex.org/C111142201","wikidata":"https://www.wikidata.org/wiki/Q818930","display_name":"Computability theory","level":2,"score":0.8278661966323853},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.7912949323654175},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.7677044868469238},{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.7444530129432678},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.7323679327964783},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7157277464866638},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.7084078192710876},{"id":"https://openalex.org/C116493835","wikidata":"https://www.wikidata.org/wiki/Q764287","display_name":"Van der Waerden's theorem","level":2,"score":0.5540909171104431},{"id":"https://openalex.org/C13851312","wikidata":"https://www.wikidata.org/wiki/Q909412","display_name":"Ordered field","level":2,"score":0.5199743509292603},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5013217926025391},{"id":"https://openalex.org/C3853638","wikidata":"https://www.wikidata.org/wiki/Q1314081","display_name":"Gap theorem","level":5,"score":0.4889947175979614},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4850853979587555},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.45862358808517456},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.4389949440956116},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3772531747817993},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28969520330429077},{"id":"https://openalex.org/C194886279","wikidata":"https://www.wikidata.org/wiki/Q430271","display_name":"Fundamental theorem","level":3,"score":0.1257152557373047},{"id":"https://openalex.org/C81150689","wikidata":"https://www.wikidata.org/wiki/Q1217677","display_name":"Fundamental theorem of calculus","level":4,"score":0.0},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2178/bsl/1182353917","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1182353917","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1182353917","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1182353917","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"pmh:oai:CiteSeerX.psu:10.1.1.648.9806","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.648.9806","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://home.gwu.edu/~harizanv/BSLHarizanov0804-001.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":80,"referenced_works":["https://openalex.org/W9167880","https://openalex.org/W93165072","https://openalex.org/W352853685","https://openalex.org/W572704962","https://openalex.org/W1489274344","https://openalex.org/W1511682313","https://openalex.org/W1518779691","https://openalex.org/W1548773247","https://openalex.org/W1554860413","https://openalex.org/W1571286435","https://openalex.org/W1575274885","https://openalex.org/W1593660953","https://openalex.org/W1597894981","https://openalex.org/W1599486919","https://openalex.org/W1601654835","https://openalex.org/W1684033657","https://openalex.org/W1964211988","https://openalex.org/W1970404779","https://openalex.org/W1970452917","https://openalex.org/W1973880596","https://openalex.org/W1974760368","https://openalex.org/W1975720205","https://openalex.org/W1976089169","https://openalex.org/W1977629364","https://openalex.org/W1978521098","https://openalex.org/W1982321417","https://openalex.org/W1982821787","https://openalex.org/W1986238564","https://openalex.org/W1987148015","https://openalex.org/W1988281938","https://openalex.org/W1990990734","https://openalex.org/W1992932719","https://openalex.org/W1996816738","https://openalex.org/W2001479515","https://openalex.org/W2004320988","https://openalex.org/W2007036268","https://openalex.org/W2010770007","https://openalex.org/W2015393409","https://openalex.org/W2023793968","https://openalex.org/W2031952547","https://openalex.org/W2034579698","https://openalex.org/W2039687554","https://openalex.org/W2044599148","https://openalex.org/W2055585831","https://openalex.org/W2056414301","https://openalex.org/W2057398815","https://openalex.org/W2062135743","https://openalex.org/W2065230732","https://openalex.org/W2070346525","https://openalex.org/W2078971842","https://openalex.org/W2079718016","https://openalex.org/W2084068730","https://openalex.org/W2086027672","https://openalex.org/W2086643971","https://openalex.org/W2106044804","https://openalex.org/W2110464795","https://openalex.org/W2132364243","https://openalex.org/W2134024760","https://openalex.org/W2142840306","https://openalex.org/W2145433104","https://openalex.org/W2146750910","https://openalex.org/W2159037930","https://openalex.org/W2165758366","https://openalex.org/W2300684981","https://openalex.org/W2329427138","https://openalex.org/W2331179602","https://openalex.org/W2333530874","https://openalex.org/W2494008706","https://openalex.org/W2498487556","https://openalex.org/W2799061192","https://openalex.org/W3187762542","https://openalex.org/W4213161523","https://openalex.org/W4231125794","https://openalex.org/W4232277851","https://openalex.org/W4246804796","https://openalex.org/W6647859553","https://openalex.org/W6679638503","https://openalex.org/W6701479315","https://openalex.org/W6702750620","https://openalex.org/W6828398953"],"related_works":["https://openalex.org/W3102609132","https://openalex.org/W4206289504","https://openalex.org/W4206028083","https://openalex.org/W2125665594","https://openalex.org/W32672360","https://openalex.org/W4254084566","https://openalex.org/W2156724103","https://openalex.org/W4286434485","https://openalex.org/W1480530468","https://openalex.org/W1614318719"],"abstract_inverted_index":{"Computable":[0],"model":[1,8,35],"theory,":[2,9],"also":[3],"called":[4],"effective":[5],"or":[6,26],"recursive":[7],"studies":[10],"algorithmic":[11,165],"properties":[12,21,166],"of":[13,29,33,44,63,74,84,160,167],"mathematical":[14,173],"structures,":[15],"their":[16],"relations,":[17],"and":[18,49,57,121,147,151,171],"isomorphisms.":[19],"These":[20],"can":[22,67],"be":[23],"described":[24],"syntactically":[25],"semantically.":[27],"One":[28],"the":[30,54,61,82,144],"major":[31],"tasks":[32],"computable":[34,65,86,94,98,140],"theory":[36,113,131,162],"is":[37,127],"to":[38,81,163],"obtain,":[39],"whenever":[40],"possible,":[41],"computability-theoretic":[42],"versions":[43],"various":[45],"classical":[46,104],"model-theoretic":[47],"notions":[48],"results.":[50],"For":[51],"example,":[52],"in":[53],"1950's,":[55],"Fr\u00f6hlich":[56],"Shepherdson":[58],"realized":[59],"that":[60,92,110,125,132],"concept":[62],"a":[64,85,97,128],"function":[66],"make":[68],"van":[69],"der":[70],"Waerden's":[71],"intuitive":[72],"notion":[73,83],"an":[75],"explicit":[76],"field":[77,95],"precise.":[78],"This":[79],"led":[80],"structure.":[87],"In":[88,143],"1960,":[89],"Rabin":[90],"proved":[91],"every":[93,103],"has":[96,114,133],"algebraic":[99],"closure.":[100],"However,":[101],"not":[102],"result":[105,123],"\u201ceffectivizes\u201d.":[106],"Unlike":[107],"Vaught's":[108],"theorem":[109],"no":[111],"complete":[112,129],"exactly":[115,134],"two":[116,135],"nonisomorphic":[117,136],"countable":[118,137],"models,":[119],"Millar's":[120],"Kudaibergenov's":[122],"establishes":[124],"there":[126],"decidable":[130],"models":[138],"with":[139],"elementary":[141],"diagrams.":[142],"1970's,":[145],"Metakides":[146],"Nerode":[148],"[58],":[149],"[59]":[150],"Remmel":[152],"[71],":[153],"[72],":[154],"[73]":[155],"used":[156],"more":[157],"advanced":[158],"methods":[159],"computability":[161],"investigate":[164],"fields,":[168],"vector":[169],"spaces,":[170],"other":[172],"structures.":[174]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
