{"id":"https://openalex.org/W2004845705","doi":"https://doi.org/10.2307/2273508","title":"Analytic determinacy and 0<sup>#</sup>","display_name":"Analytic determinacy and 0<sup>#</sup>","publication_year":1978,"publication_date":"1978-12-01","ids":{"openalex":"https://openalex.org/W2004845705","doi":"https://doi.org/10.2307/2273508","mag":"2004845705"},"language":"en","primary_location":{"id":"doi:10.2307/2273508","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273508","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/A5103437344","display_name":"Leo Harrington","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Leo Harrington","raw_affiliation_strings":["University of California at Berkeley Berkeley, California 94720","University of California at Berkeley, Berkeley, California 94720"],"affiliations":[{"raw_affiliation_string":"University of California at Berkeley Berkeley, California 94720","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"University of California at Berkeley, Berkeley, California 94720","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103437344"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":29.6944,"has_fulltext":false,"cited_by_count":196,"citation_normalized_percentile":{"value":0.99442652,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"43","issue":"4","first_page":"685","last_page":"693"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9771000146865845,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9771000146865845,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.960099995136261,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9114000201225281,"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":0.9610321521759033},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.8131970167160034},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7512926459312439},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.48771223425865173},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4592973291873932},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4363194406032562},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3401772975921631},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15618997812271118}],"concepts":[{"id":"https://openalex.org/C58468513","wikidata":"https://www.wikidata.org/wiki/Q1201165","display_name":"Determinacy","level":2,"score":0.9610321521759033},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.8131970167160034},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7512926459312439},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.48771223425865173},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4592973291873932},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4363194406032562},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3401772975921631},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15618997812271118},{"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:10.2307/2273508","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273508","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.46000000834465027,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W65053296","https://openalex.org/W568910110","https://openalex.org/W1221529125","https://openalex.org/W1515759392","https://openalex.org/W1554691866","https://openalex.org/W1886820163","https://openalex.org/W1965874532","https://openalex.org/W1985995199","https://openalex.org/W2015103007","https://openalex.org/W2021406081","https://openalex.org/W2081160992","https://openalex.org/W2117832390","https://openalex.org/W2530006810","https://openalex.org/W2905135108","https://openalex.org/W4291439952"],"related_works":["https://openalex.org/W3037524176","https://openalex.org/W2387449261","https://openalex.org/W1521335825","https://openalex.org/W2505787881","https://openalex.org/W2418518962","https://openalex.org/W4301421734","https://openalex.org/W2063305408","https://openalex.org/W4239791835","https://openalex.org/W2588434364","https://openalex.org/W1993569943"],"abstract_inverted_index":{"Martin":[0,59,96],"[12]":[1],"has":[2,97],"shown":[3,99],"that":[4,100],"the":[5,14,22,63,81,85,101,118,172,178,191],"determinacy":[6],"of":[7,13,16,24,46,65,84,103,126,156,165,174],"analytic":[8,28],"games":[9,29],"is":[10,21,80],"a":[11,52,154],"consequence":[12],"existence":[15,64,102],"sharps.":[17],"Our":[18,114],"main":[19],"result":[20],"converse":[23,140],"this:":[25],"Theorem.":[26,120],"If":[27,121],"are":[30,128],"determined,":[31],"then":[32,131],"x":[33,39,137,220,225,234,239],"2":[34,108,240],"exists":[35,133],"for":[36,134,214,222],"all":[37,122,135,223],"reals":[38,127,136,224],".":[40,138,241],"This":[41],"theorem":[42,143],"answers":[43],"question":[44],"80":[45],"Friedman":[47],"[5].":[48],"We":[49,152],"actually":[50],"obtain":[51],"somewhat":[53],"sharper":[54],"result;":[55],"see":[56,94],"Theorem":[57],"4.1.":[58],"had":[60,144],"previously":[61,146],"deduced":[62],"sharps":[66,104],"from":[67],"3":[68],"\u2212":[69,76,90,109],"\u03a0":[70,77,91,110],"1":[71,72,78,79,92,93,111,112],"-determinacy":[73],"(where":[74],"\u03b1":[75],"\u03b1th":[82],"level":[83],"difference":[86],"hierarchy":[87],"based":[88],"on":[89],"[1]).":[95],"also":[98,116],"implies":[105],"&lt;":[106],"\u03c9":[107],"-determinacy.":[113],"method":[115],"produces":[117],"following:":[119],"analytic,":[123],"non-Borel":[124],"sets":[125],"Borel":[129],"isomorphic,":[130],"x*":[132],"The":[139],"to":[141,158,231],"this":[142,189,205],"been":[145],"proven":[147],"by":[148],"Steel":[149],"[7],":[150],"[18].":[151],"owe":[153],"debt":[155],"gratitude":[157],"Ramez":[159],"Sami":[160],"and":[161,182,200],"John":[162],"Steel,":[163],"some":[164],"whose":[166],"ideas":[167],"form":[168],"basic":[169],"components":[170],"in":[171],"proofs":[173],"our":[175,229],"results.":[176],"For":[177],"various":[179],"notation,":[180],"definitions":[181],"theorems":[183],"which":[184],"we":[185,207],"will":[186,208],"assume":[187],"throughout":[188],"paper,":[190],"reader":[192],"should":[193],"consult":[194],"[3,":[195],"\u00a7\u00a75,":[196],"17],":[197],"[8],":[198],"[13]":[199],"[14,":[201],"Chapter":[202],"16].":[203],"Throughout":[204],"paper":[206],"concern":[209],"ourselves":[210],"only":[211],"with":[212],"methods":[213],"obtaining":[215],"0":[216],"#":[217,221],"(rather":[218],"than":[219],").":[226],"By":[227],"relativizing":[228],"arguments":[230],"each":[232],"real":[233],",":[235],"one":[236],"can":[237],"produce":[238]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":19},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
