{"id":"https://openalex.org/W2579145955","doi":"https://doi.org/10.2307/421049","title":"Two Applications of Inner Model Theory to the Study of Sets","display_name":"Two Applications of Inner Model Theory to the Study of Sets","publication_year":1996,"publication_date":"1996-03-01","ids":{"openalex":"https://openalex.org/W2579145955","doi":"https://doi.org/10.2307/421049","mag":"2579145955"},"language":"en","primary_location":{"id":"doi:10.2307/421049","is_oa":false,"landing_page_url":"https://doi.org/10.2307/421049","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/A5044036779","display_name":"Greg Hjorth","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Greg Hjorth","raw_affiliation_strings":["Department of mathematics, University of California, Los Angeles, Los Angeles, CA 90095-1555, USAE-mail:","Department of mathematics, University of California, Los Angeles, Los Angeles, CA 90095-1555, USA E-mail/i: , greg@math.ucla.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of mathematics, University of California, Los Angeles, Los Angeles, CA 90095-1555, USAE-mail:","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of mathematics, University of California, Los Angeles, Los Angeles, CA 90095-1555, USA E-mail/i: , greg@math.ucla.edu","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044036779"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":null,"apc_paid":null,"fwci":1.4572,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.83089983,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"2","issue":"1","first_page":"94","last_page":"107"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9995999932289124,"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":0.9995999932289124,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9918000102043152,"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/T10258","display_name":"Philosophy and Theoretical Science","score":0.9878000020980835,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/determinacy","display_name":"Determinacy","score":0.9690450429916382},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7110799551010132},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6822436451911926},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.6751124858856201},{"id":"https://openalex.org/keywords/core-model","display_name":"Core model","score":0.5850203633308411},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.5296979546546936},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5206369757652283},{"id":"https://openalex.org/keywords/model-theory","display_name":"Model theory","score":0.4908466935157776},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4677700400352478},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44604671001434326},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3615773916244507},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14820638298988342},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06472870707511902}],"concepts":[{"id":"https://openalex.org/C58468513","wikidata":"https://www.wikidata.org/wiki/Q1201165","display_name":"Determinacy","level":2,"score":0.9690450429916382},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7110799551010132},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6822436451911926},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.6751124858856201},{"id":"https://openalex.org/C2780366209","wikidata":"https://www.wikidata.org/wiki/Q5170200","display_name":"Core model","level":2,"score":0.5850203633308411},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.5296979546546936},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5206369757652283},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.4908466935157776},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4677700400352478},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44604671001434326},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3615773916244507},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14820638298988342},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06472870707511902},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/421049","is_oa":false,"landing_page_url":"https://doi.org/10.2307/421049","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W143478684","https://openalex.org/W196306359","https://openalex.org/W1139854568","https://openalex.org/W1465001547","https://openalex.org/W1555991696","https://openalex.org/W1602868010","https://openalex.org/W1608887313","https://openalex.org/W1971511826","https://openalex.org/W1972147845","https://openalex.org/W1991271290","https://openalex.org/W2004845705","https://openalex.org/W2018919209","https://openalex.org/W2056715322","https://openalex.org/W2081278058","https://openalex.org/W2120939240","https://openalex.org/W2478289388","https://openalex.org/W2482283928","https://openalex.org/W4230295967","https://openalex.org/W4235955922","https://openalex.org/W4302414399","https://openalex.org/W6643169103","https://openalex.org/W6670892948"],"related_works":["https://openalex.org/W2980985936","https://openalex.org/W57194850","https://openalex.org/W2034208759","https://openalex.org/W1574825745","https://openalex.org/W2151251236","https://openalex.org/W2016661762","https://openalex.org/W1997033389","https://openalex.org/W1877127512","https://openalex.org/W2579145955","https://openalex.org/W3127283155"],"abstract_inverted_index":{"\u00a70.":[0],"Preface":[1],".":[2,148],"There":[3,155],"has":[4],"been":[5],"an":[6,156],"expectation":[7],"that":[8,62,120,172,220,249],"the":[9,12,18,28,36,45,53,56,88,96,105,113,169,186,189,200,232,237,241],"endgame":[10],"of":[11,23,38,47,68,115,137,158,183,188,217,227,236,243,246,253],"more":[13],"tenacious":[14],"problems":[15],"raised":[16],"by":[17,102,153],"Los":[19],"Angeles":[20],"\u2018cabal\u2019":[21],"school":[22],"descriptive":[24,48,77],"set":[25,49,78],"theory":[26,108,164,219],"in":[27,44,60],"1970's":[29],"should":[30],"ultimately":[31],"be":[32,222],"played":[33],"out":[34],"with":[35],"use":[37],"inner":[39,162,247],"model":[40,107,163],"theory.":[41],"Questions":[42],"phrased":[43],"language":[46],"theory,":[50],"where":[51,104],"both":[52],"conclusions":[54],"and":[55,70,92,117,161,204],"assumptions":[57,198],"are":[58,128,213],"couched":[59],"terms":[61],"only":[63,193],"mention":[64],"simply":[65],"definable":[66],"sets":[67,191],"reals,":[69],"which":[71],"have":[72],"proved":[73,223],"resistant":[74],"to":[75,111,167,180,231],"purely":[76],"theoretic":[79],"arguments,":[80],"may":[81,208],"at":[82],"last":[83],"find":[84,181],"their":[85],"solution":[86],"through":[87],"connection":[89],"between":[90,202],"determinacy":[91,173,197,203],"large":[93,159,205,233,254],"cardinals.":[94,206,255],"Perhaps":[95],"most":[97],"striking":[98],"example":[99],"was":[100,109],"given":[101,251],"[24],":[103],"core":[106],"used":[110,166],"analyze":[112],"structure":[114,187],"HOD":[116,141],"then":[118],"show":[119],"all":[121],"regular":[122],"cardinals":[123,160],"below":[124],"\u0398":[125],"L":[126,142],"(\u211d)":[127,143],"measurable.":[129],"John":[130],"Steel's":[131],"analysis":[132],"also":[133],"settled":[134],"a":[135],"number":[136,218],"structural":[138],"questions":[139],"regarding":[140,185],",":[144],"such":[145,239],"as":[146,240],"GCH":[147],"Another":[149],"illustration":[150],"is":[151,165,178],"provided":[152],"[21].":[154],"application":[157],"generalize":[168],"Harrington-Martin":[170],"theorem":[171],"implies":[174],")determinacy.":[175],"However,":[176],"it":[177],"harder":[179],"examples":[182],"theorems":[184],"projective":[190,228],"whose":[192],"known":[194],"proof":[195],"from":[196],"uses":[199],"link":[201],"We":[207],"equivalently":[209],"ask":[210],"whether":[211],"there":[212],"second":[214],"order":[215],"statements":[216],"cannot":[221],"under":[224],"PD\u2013the":[225],"axiom":[226],"determinacy\u2013without":[229],"appealing":[230],"cardinal":[234],"consequences":[235],"PD,":[238],"existence":[242],"certain":[244],"kinds":[245],"models":[248],"contain":[250],"types":[252]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
