{"id":"https://openalex.org/W2152456478","doi":"https://doi.org/10.2307/2275544","title":"Completeness of global intuitionistic set theory","display_name":"Completeness of global intuitionistic set theory","publication_year":1997,"publication_date":"1997-06-01","ids":{"openalex":"https://openalex.org/W2152456478","doi":"https://doi.org/10.2307/2275544","mag":"2152456478"},"language":"en","primary_location":{"id":"doi:10.2307/2275544","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275544","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/A5026388153","display_name":"Satoko Titani","orcid":null},"institutions":[{"id":"https://openalex.org/I184937672","display_name":"Chubu University","ror":"https://ror.org/02sps0775","country_code":"JP","type":"education","lineage":["https://openalex.org/I184937672"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Satoko Titani","raw_affiliation_strings":["Department of Mathematics, Chubu University, Kasugai, Aichi 487, Japan, E-mail:","Department of Mathematics, Chubu University, Kasugai, Aichi 487, Japan, E-mail: titani@isc.chubu.ac.jp"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chubu University, Kasugai, Aichi 487, Japan, E-mail:","institution_ids":["https://openalex.org/I184937672"]},{"raw_affiliation_string":"Department of Mathematics, Chubu University, Kasugai, Aichi 487, Japan, E-mail: titani@isc.chubu.ac.jp","institution_ids":["https://openalex.org/I184937672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026388153"],"corresponding_institution_ids":["https://openalex.org/I184937672"],"apc_list":null,"apc_paid":null,"fwci":1.1971,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.84288679,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"62","issue":"2","first_page":"506","last_page":"528"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.996999979019165,"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/metatheory","display_name":"Metatheory","score":0.7829746007919312},{"id":"https://openalex.org/keywords/truth-value","display_name":"Truth value","score":0.6933770179748535},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.6177695989608765},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.598263144493103},{"id":"https://openalex.org/keywords/sentence","display_name":"Sentence","score":0.5865302681922913},{"id":"https://openalex.org/keywords/symbol","display_name":"Symbol (formal)","score":0.5652413368225098},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.5178002119064331},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5160348415374756},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43887773156166077},{"id":"https://openalex.org/keywords/first-order-logic","display_name":"First-order logic","score":0.43707507848739624},{"id":"https://openalex.org/keywords/classical-logic","display_name":"Classical logic","score":0.4356977641582489},{"id":"https://openalex.org/keywords/many-valued-logic","display_name":"Many-valued logic","score":0.43008846044540405},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41390740871429443},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.37923628091812134},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3701275587081909},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35097450017929077},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.25470098853111267},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2376759648323059},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.2262357473373413},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20673319697380066},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.11900439858436584},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09424245357513428}],"concepts":[{"id":"https://openalex.org/C39387531","wikidata":"https://www.wikidata.org/wiki/Q1096708","display_name":"Metatheory","level":2,"score":0.7829746007919312},{"id":"https://openalex.org/C46274116","wikidata":"https://www.wikidata.org/wiki/Q185521","display_name":"Truth value","level":2,"score":0.6933770179748535},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.6177695989608765},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.598263144493103},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.5865302681922913},{"id":"https://openalex.org/C134400042","wikidata":"https://www.wikidata.org/wiki/Q2372244","display_name":"Symbol (formal)","level":2,"score":0.5652413368225098},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.5178002119064331},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5160348415374756},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43887773156166077},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.43707507848739624},{"id":"https://openalex.org/C32241873","wikidata":"https://www.wikidata.org/wiki/Q236975","display_name":"Classical logic","level":2,"score":0.4356977641582489},{"id":"https://openalex.org/C150889026","wikidata":"https://www.wikidata.org/wiki/Q185502","display_name":"Many-valued logic","level":3,"score":0.43008846044540405},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41390740871429443},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.37923628091812134},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3701275587081909},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35097450017929077},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.25470098853111267},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2376759648323059},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.2262357473373413},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20673319697380066},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.11900439858436584},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09424245357513428},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2275544","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275544","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"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183745240","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745240","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W115176759","https://openalex.org/W2026053661","https://openalex.org/W2317097801","https://openalex.org/W3039529476"],"related_works":["https://openalex.org/W10948657","https://openalex.org/W2508249339","https://openalex.org/W4223889865","https://openalex.org/W2530278950","https://openalex.org/W1537466439","https://openalex.org/W2897239477","https://openalex.org/W2036407372","https://openalex.org/W1973501176","https://openalex.org/W2792899210","https://openalex.org/W1986625420"],"abstract_inverted_index":{"Gentzen's":[0],"sequential":[1],"system":[2,31,89],"LJ":[3,32,90],"of":[4,10,107,165,168],"intuitionistic":[5,114,129,138],"logic":[6],"has":[7],"two":[8],"symbols":[9,42,173],"implication.":[11],"One":[12],"is":[13,21,55,63,68,78,102,110,148,195,223],"the":[14,19,22,29,40,73,87,92,146,171,190,206],"logical":[15,30,41,88,172,216],"symbol":[16,24,208],"\u2192":[17],"and":[18,53,123,189],"other":[20,83],"metalogical":[23,65,207],"\u21d2":[25,54,61,100,193,209,221],"in":[26,91,97],"sequents":[27],"Considering":[28],"as":[33,185,197,214,225],"a":[34,56,64,79,103,156,161,166,215],"mathematical":[35],"object,":[36],"we":[37,85,126,143],"understand":[38],"that":[39,75,145,205,219],"\u2227,":[43,174],"\u2228,":[44,175],"\u2192,":[45,176],"\u00ac,":[46,177],"\u2200,":[47],"\u2203":[48,181],"are":[49,183],"operators":[50,186,217],"on":[51,72,137,150,187],"formulas,":[52],"relation.":[57],"That":[58],"is,":[59],"\u03c6":[60,99,192,220],"\u03a8":[62,101,194,222],"sentence":[66,191],"which":[67,98],"true":[69],"or":[70,200,227],"false,":[71],"understanding":[74],"our":[76],"metalogic":[77],"classical":[80,93,151],"logic.":[81,139,152],"In":[82,121,140],"words,":[84],"discuss":[86],"set":[94,115,130,164],"theory":[95,116,131],"ZFC,":[96],"sentence.":[104],"The":[105],"aim":[106],"this":[108,141],"paper":[109,142],"to":[111],"formulate":[112],"an":[113,128],"together":[117,132],"with":[118,133],"its":[119,134],"metatheory.":[120],"Takeuti":[122],"Titani":[124],"[6],":[125],"formulated":[127],"metatheory":[135,147],"based":[136,149],"postulate":[144],"Let":[153],"\u03a9":[154,158],"be":[155,160,212],"cHa.":[157],"can":[159,211],"truth":[162],"value":[163],"model":[167],"LJ.":[169],"Then":[170],"\u2200":[178],"x":[179,182],",":[180],"interpreted":[184,196,224],"\u03a9,":[188],"1":[198,226],"(true)":[199],"0":[201],"(false).":[202],"This":[203],"means":[204],"also":[210],"expressed":[213],"such":[218],"0.":[228]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
