{"id":"https://openalex.org/W1971511826","doi":"https://doi.org/10.2307/421159","title":"Optimal Proofs of Determinacy","display_name":"Optimal Proofs of Determinacy","publication_year":1995,"publication_date":"1995-09-01","ids":{"openalex":"https://openalex.org/W1971511826","doi":"https://doi.org/10.2307/421159","mag":"1971511826"},"language":"en","primary_location":{"id":"doi:10.2307/421159","is_oa":false,"landing_page_url":"https://doi.org/10.2307/421159","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/A5072283323","display_name":"Itay Neeman","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":"Itay Neeman","raw_affiliation_strings":["Department of Mathematics, University of California, Los Angeles, CA 90024. E-mail:","Department of Mathematics, University of California, Los Angeles, CA 90024. E-mail: ineeman@math.ucla.edu"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles, CA 90024. E-mail:","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles, CA 90024. E-mail: ineeman@math.ucla.edu","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5072283323"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":null,"apc_paid":null,"fwci":1.6657,"has_fulltext":false,"cited_by_count":74,"citation_normalized_percentile":{"value":0.80789022,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"1","issue":"3","first_page":"327","last_page":"339"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9958000183105469,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/determinacy","display_name":"Determinacy","score":0.9803642630577087},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.8537155389785767},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6175074577331543},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.5245226621627808},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4945637881755829},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48720163106918335},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.4834533631801605},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.41418391466140747},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37279123067855835},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23389017581939697},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06468936800956726}],"concepts":[{"id":"https://openalex.org/C58468513","wikidata":"https://www.wikidata.org/wiki/Q1201165","display_name":"Determinacy","level":2,"score":0.9803642630577087},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8537155389785767},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6175074577331543},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.5245226621627808},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4945637881755829},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48720163106918335},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4834533631801605},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.41418391466140747},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37279123067855835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23389017581939697},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06468936800956726},{"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:10.2307/421159","is_oa":false,"landing_page_url":"https://doi.org/10.2307/421159","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W56237695","https://openalex.org/W2004845705","https://openalex.org/W2007638330","https://openalex.org/W2043378229","https://openalex.org/W2049652789","https://openalex.org/W4230295967","https://openalex.org/W4235955922"],"related_works":["https://openalex.org/W2588434364","https://openalex.org/W2019604532","https://openalex.org/W1601745317","https://openalex.org/W2753083100","https://openalex.org/W3198799031","https://openalex.org/W2090831035","https://openalex.org/W1584952351","https://openalex.org/W2081948323","https://openalex.org/W2927058411","https://openalex.org/W3005084276"],"abstract_inverted_index":{"In":[0],"this":[1,110],"paper":[2],"I":[3],"shall":[4],"present":[5],"a":[6,49,124,130,136,213,235],"method":[7,42],"for":[8,64],"proving":[9,159],"determinacy":[10,36,56,66,132,219],"from":[11],"large":[12,80,149,181,230,248],"cardinals":[13,81,182],"which,":[14],"in":[15,57],"many":[16],"cases,":[17],"seems":[18],"to":[19,47,75,94,247],"yield":[20],"optimal":[21,65],"results.":[22],"One":[23],"of":[24,30,52,91,104,109,123,142,148,177,205,209,215,218],"the":[25,38,77,97,112,140,143,178,216],"main":[26],"applications":[27],"extends":[28],"theorems":[29],"Martin,":[31],"Steel":[32],"and":[33,82,99,134,166,183,202,244],"Woodin":[34,206,222],"about":[35,55,207],"within":[37],"projective":[39],"hierarchy.":[40],"The":[41,60],"can":[43],"also":[44,233],"be":[45],"used":[46],"give":[48],"new":[50],"proof":[51,114,152,189],"Woodin's":[53],"theorem":[54,126,144],"L":[58,192,196],"(\u211d).":[59],"reason":[61],"we":[62],"look":[63],"proofs":[67,73,226],"is":[68,111,120],"not":[69,227],"only":[70,228],"vanity.":[71],"Such":[72],"serve":[74],"tighten":[76],"connection":[78,179,238],"between":[79,180,239],"descriptive":[83,184,240],"set":[84,185,241],"theory,":[85],"letting":[86],"us":[87],"bring":[88],"our":[89,102],"knowledge":[90],"one":[92],"subject":[93],"bear":[95],"on":[96],"other,":[98],"thus":[100],"increasing":[101],"understanding":[103],"both.":[105],"A":[106],"classic":[107],"example":[108,122],"Harrington-Martin":[113],"that":[115,160,168,190],"-determinacy":[116,161,173],"implies":[117],"-determinacy.":[118],"This":[119],"an":[121],"transfer":[125],",":[127,157,212],"which":[128,221],"assumes":[129],"certain":[131],"hypothesis":[133],"proves":[135],"stronger":[137],"one.":[138],"While":[139],"statement":[141],"makes":[145],"no":[146],"mention":[147],"cardinals,":[150,231],"its":[151],"goes":[153],"through":[154],"0":[155,163,169],"#":[156,164,170],"first":[158],"\u21d2":[162,172,194],"exists,":[165],"then":[167],"exists":[171],"More":[174],"recent":[175],"examples":[176],"theory":[186],"include":[187],"Steel's":[188],"AD":[191,210,220],"(\u211d)":[193,197],"HOD":[195],"\u22a8":[198],"GCH,":[199],"see":[200],"[9],":[201],"several":[203],"results":[204],"models":[208],"+":[211],"strengthening":[214],"axiom":[217],"has":[223],"introduced.":[224],"These":[225],"use":[229],"but":[232],"reveal":[234],"deep,":[236],"structural":[237],"theoretic":[242],"notions":[243,245],"related":[246],"cardinals.":[249]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":18},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2026-03-03T06:13:14.889584","created_date":"2025-10-10T00:00:00"}