{"id":"https://openalex.org/W2094562124","doi":"https://doi.org/10.2178/bsl/1185803804","title":"G\u00f6del and Set Theory","display_name":"G\u00f6del and Set Theory","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W2094562124","doi":"https://doi.org/10.2178/bsl/1185803804","mag":"2094562124"},"language":"en","primary_location":{"id":"doi:10.2178/bsl/1185803804","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1185803804","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/A5050426319","display_name":"Akihiro Kanamori","orcid":null},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Akihiro Kanamori","raw_affiliation_strings":["Department of Mathematics, Boston University, Boston, Massachusetts 02215, USAE-mail:","Department of Mathematics, Boston University, Boston, Massachusetts 02215, USA E-mail/i: aki@math.bu.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Boston University, Boston, Massachusetts 02215, USAE-mail:","institution_ids":["https://openalex.org/I111088046"]},{"raw_affiliation_string":"Department of Mathematics, Boston University, Boston, Massachusetts 02215, USA E-mail/i: aki@math.bu.edu","institution_ids":["https://openalex.org/I111088046"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050426319"],"corresponding_institution_ids":["https://openalex.org/I111088046"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.8252,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.71183024,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"13","issue":"2","first_page":"153","last_page":"188"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10258","display_name":"Philosophy and Theoretical Science","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10778","display_name":"Philosophy and History of Science","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/universal-set","display_name":"Universal set","score":0.6768024563789368},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.6320675015449524},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.5990502238273621},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.563186764717102},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.5208131074905396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5147954821586609},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.48745226860046387},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.458721399307251},{"id":"https://openalex.org/keywords/foundations-of-mathematics","display_name":"Foundations of mathematics","score":0.4510388970375061},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4368482232093811},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.4203702211380005},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.4129233658313751},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2974837124347687},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.26590657234191895},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.21921145915985107}],"concepts":[{"id":"https://openalex.org/C102565666","wikidata":"https://www.wikidata.org/wiki/Q1378301","display_name":"Universal set","level":3,"score":0.6768024563789368},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.6320675015449524},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.5990502238273621},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.563186764717102},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.5208131074905396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5147954821586609},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.48745226860046387},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.458721399307251},{"id":"https://openalex.org/C183140480","wikidata":"https://www.wikidata.org/wiki/Q833585","display_name":"Foundations of mathematics","level":2,"score":0.4510388970375061},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4368482232093811},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.4203702211380005},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.4129233658313751},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2974837124347687},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.26590657234191895},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.21921145915985107},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/1185803804","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1185803804","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:CiteSeerX.psu:10.1.1.72.8003","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.72.8003","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.bu.edu/people/aki/13.pdf","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1185803804","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1185803804","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":82,"referenced_works":["https://openalex.org/W81494948","https://openalex.org/W154666901","https://openalex.org/W277532062","https://openalex.org/W586528178","https://openalex.org/W649681871","https://openalex.org/W788058594","https://openalex.org/W820565775","https://openalex.org/W875972856","https://openalex.org/W943508897","https://openalex.org/W951600495","https://openalex.org/W968932919","https://openalex.org/W1476448305","https://openalex.org/W1486519940","https://openalex.org/W1489096776","https://openalex.org/W1497264647","https://openalex.org/W1537390618","https://openalex.org/W1555643099","https://openalex.org/W1555991696","https://openalex.org/W1563087464","https://openalex.org/W1567156820","https://openalex.org/W1568406216","https://openalex.org/W1577168440","https://openalex.org/W1607953571","https://openalex.org/W1629174050","https://openalex.org/W1781706428","https://openalex.org/W1892591292","https://openalex.org/W1970524747","https://openalex.org/W1979632868","https://openalex.org/W1987695878","https://openalex.org/W1991697528","https://openalex.org/W1993653064","https://openalex.org/W2000854556","https://openalex.org/W2016700453","https://openalex.org/W2022040382","https://openalex.org/W2033225733","https://openalex.org/W2038389031","https://openalex.org/W2045439583","https://openalex.org/W2053454736","https://openalex.org/W2060878518","https://openalex.org/W2064028777","https://openalex.org/W2067674877","https://openalex.org/W2073171092","https://openalex.org/W2075458778","https://openalex.org/W2092726141","https://openalex.org/W2101836517","https://openalex.org/W2106131771","https://openalex.org/W2109492210","https://openalex.org/W2114804254","https://openalex.org/W2117873821","https://openalex.org/W2118148896","https://openalex.org/W2122092051","https://openalex.org/W2152688519","https://openalex.org/W2163568292","https://openalex.org/W2220946013","https://openalex.org/W2328065520","https://openalex.org/W2403653109","https://openalex.org/W2478289388","https://openalex.org/W2489785608","https://openalex.org/W2501639037","https://openalex.org/W2567810018","https://openalex.org/W2601523163","https://openalex.org/W2958814800","https://openalex.org/W3152741257","https://openalex.org/W3198736518","https://openalex.org/W4206380161","https://openalex.org/W4230295967","https://openalex.org/W4234684401","https://openalex.org/W4246326106","https://openalex.org/W4256084764","https://openalex.org/W4256369010","https://openalex.org/W4388156054","https://openalex.org/W4388156116","https://openalex.org/W4388432759","https://openalex.org/W4388433027","https://openalex.org/W4388433037","https://openalex.org/W6617428170","https://openalex.org/W6658831528","https://openalex.org/W6713197628","https://openalex.org/W6722993700","https://openalex.org/W6735779031","https://openalex.org/W6801199449","https://openalex.org/W7056227344"],"related_works":["https://openalex.org/W1574825745","https://openalex.org/W102647493","https://openalex.org/W2500725777","https://openalex.org/W3197691547","https://openalex.org/W2079743999","https://openalex.org/W118173783","https://openalex.org/W1984427300","https://openalex.org/W4391120945","https://openalex.org/W177504871","https://openalex.org/W2055120637"],"abstract_inverted_index":{"Kurt":[0],"G\u00f6del":[1,55,75,225],"(1906\u20131978)":[2],"with":[3,63,92],"his":[4,136,155,232],"work":[5,124,180,202,209],"on":[6,77],"the":[7,10,14,20,28,34,46,51,101,106,132,147,162,170,175,188,196],"constructible":[8],"universeLestablished":[9],"relative":[11],"consistency":[12],"of":[13,16,30,39,50,53,70,80,103,105,108,114,120,146,164,181,191,234],"Axiom":[15],"Choice":[17],"(AC)":[18],"and":[19,36,44,60,67,84,149,159,177,183,185,222,229],"Continuum":[21],"Hypothesis":[22],"(CH).":[23],"More":[24],"broadly,":[25],"he":[26],"ensured":[27],"ascendancy":[29],"first-order":[31],"logic":[32],"as":[33,111,152,193],"framework":[35],"a":[37,78,112],"matter":[38,66],"method":[40],"for":[41,211],"set":[42,58,81,109,126,212,235],"theory":[43,59,110,236],"secured":[45],"cumulative":[47],"hierarchy":[48],"view":[49,104,145],"universe":[52],"sets.":[54],"thereby":[56],"transformed":[57],"launched":[61],"it":[62],"structured":[64],"subject":[65],"specific":[68],"methods":[69],"proof.":[71],"In":[72],"later":[73],"years":[74],"worked":[76],"variety":[79],"theoretic":[82],"constructions":[83],"speculated":[85],"about":[86,122],"how":[87,206,230],"problems":[88],"might":[89],"be":[90],"settled":[91],"new":[93],"axioms.":[94],"We":[95,200],"here":[96],"chronicle":[97],"this":[98],"development":[99,151],"from":[100,128],"point":[102],"evolution":[107],"field":[113],"mathematics.":[115,171],"Much":[116],"has":[117],"been":[118],"written,":[119],"course,":[121],"G\u00f6del's":[123,208],"in":[125,179,195],"theory,":[127],"textbook":[129],"expositions":[130],"to":[131,135,218,227],"introductory":[133],"notes":[134],"collected":[137],"papers.":[138],"The":[139],"present":[140],"account":[141],"presents":[142],"an":[143],"integrated":[144],"historical":[148],"mathematical":[150],"supported":[153],"by":[154],"recently":[156],"published":[157],"lectures":[158],"correspondence.":[160],"Beyond":[161],"surface":[163],"things":[165],"we":[166],"delve":[167],"deeper":[168],"into":[169],"What":[172],"emerges":[173],"are":[174],"roots":[176],"anticipations":[178],"Russell":[182],"Hilbert,":[184],"most":[186],"prominently":[187],"sustained":[189],"motif":[190],"truth":[192],"formalizable":[194],"\u201cnext":[197],"higher":[198],"system\u201d.":[199],"especially":[201],"at":[203],"bringing":[204],"out":[205],"transforming":[207],"was":[210],"theory.":[213],"It":[214],"is":[215],"difficult":[216],"now":[217],"see":[219],"what":[220],"conceptual":[221],"technical":[223],"distance":[224],"had":[226],"cover":[228],"dramatic":[231],"re-orientation":[233],"was.":[237]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}