{"id":"https://openalex.org/W2105293318","doi":"https://doi.org/10.2307/2586857","title":"An absoluteness principle for Borel sets","display_name":"An absoluteness principle for Borel sets","publication_year":1998,"publication_date":"1998-06-01","ids":{"openalex":"https://openalex.org/W2105293318","doi":"https://doi.org/10.2307/2586857","mag":"2105293318"},"language":"en","primary_location":{"id":"doi:10.2307/2586857","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586857","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":"The 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/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"]},{"id":"https://openalex.org/I2803209242","display_name":"University of California System","ror":"https://ror.org/00pjdza24","country_code":"US","type":"education","lineage":["https://openalex.org/I2803209242"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Greg Hjorth","raw_affiliation_strings":["Mathematics Department, University of California, Los Angeles, Los Angeles, California 90095-1555, USA, E-mail:","University of California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of California, Los Angeles, Los Angeles, California 90095-1555, USA, E-mail:","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"University of California","institution_ids":["https://openalex.org/I2803209242"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044036779"],"corresponding_institution_ids":["https://openalex.org/I161318765","https://openalex.org/I2803209242"],"apc_list":null,"apc_paid":null,"fwci":2.3291,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.88135324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"63","issue":"2","first_page":"663","last_page":"693"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9925000071525574,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9726999998092651,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/absoluteness","display_name":"Absoluteness","score":0.9875903725624084},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6991258263587952},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.6796389818191528},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.44970935583114624},{"id":"https://openalex.org/keywords/stern","display_name":"Stern","score":0.44752514362335205},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.42816638946533203},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3347625434398651},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.25658929347991943},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.12293770909309387},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07830092310905457}],"concepts":[{"id":"https://openalex.org/C2780102774","wikidata":"https://www.wikidata.org/wiki/Q4669873","display_name":"Absoluteness","level":2,"score":0.9875903725624084},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6991258263587952},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.6796389818191528},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.44970935583114624},{"id":"https://openalex.org/C96597354","wikidata":"https://www.wikidata.org/wiki/Q273062","display_name":"Stern","level":2,"score":0.44752514362335205},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.42816638946533203},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3347625434398651},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.25658929347991943},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.12293770909309387},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07830092310905457},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199104240","wikidata":"https://www.wikidata.org/wiki/Q118291","display_name":"Marine engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2586857","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586857","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":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183745527","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745527","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1555991696","https://openalex.org/W1602868010","https://openalex.org/W1860088429","https://openalex.org/W1969555173","https://openalex.org/W1970364998","https://openalex.org/W1978325228","https://openalex.org/W1991271290","https://openalex.org/W2008010911","https://openalex.org/W2018919209","https://openalex.org/W2024078235","https://openalex.org/W2074533872","https://openalex.org/W2077049921","https://openalex.org/W2079152571","https://openalex.org/W2081278058","https://openalex.org/W2093587077","https://openalex.org/W2131429076","https://openalex.org/W2163355682","https://openalex.org/W4230295967","https://openalex.org/W4243480862","https://openalex.org/W6670892948","https://openalex.org/W6679851780"],"related_works":["https://openalex.org/W2055613065","https://openalex.org/W4286816173","https://openalex.org/W2949695231","https://openalex.org/W2106142172","https://openalex.org/W2030570356","https://openalex.org/W1513191254","https://openalex.org/W137873688","https://openalex.org/W2913228604","https://openalex.org/W2104913734","https://openalex.org/W2280165579"],"abstract_inverted_index":{"The":[0,75,106,140],"purpose":[1],"of":[2,23,96,112,131,142,152,162,193,226,236,271,280],"these":[3],"notes":[4],"is":[5,147,230,288],"to":[6,12,19,109,117,158,198,201,209],"describe":[7],"an":[8,160],"absoluteness":[9,47,217,273],"principle":[10,48],"due":[11],"Jacques":[13],"Stern":[14],"and":[15,78,205,264,268],"discuss":[16],"some":[17,70,123],"applications":[18],"the":[20,41,59,94,110,129,149,153,224,234,254],"general":[21],"study":[22],"Borel":[24,42,97,255],"sets.":[25,114,133],"This":[26],"paper":[27],"will":[28,81,207,276],"not":[29],"be":[30,56,67,82,167,181,199,220,260],"engaged":[31],"in":[32,36,84,122,223,249],"independence":[33,237],"results,":[34,238],"but":[35],"proving":[37,250],"outright":[38],"theorems":[39,252,282],"about":[40,253],"hierarchy.":[43,256],"Roughly":[44],"speaking,":[45],"Stern's":[46,216,244,272],"states":[49],"that":[50,172,196,243],"if":[51,176],"a":[52,89,177,191,278],"certain":[53,174],"set":[54,155,179],"can":[55,66,170,180,218],"introduced":[57,68,182],"into":[58],"universe":[60],"by":[61,69,128,183],"forcing":[62,72,145,229],",":[63,77],"then":[64,185],"it":[65,186],"small":[71,138,144],"notion":[73,146],".":[74,105],"notation":[76],"so":[79],"on,":[80],"defined":[83],"Section":[85],"1;":[86],"this":[87,126,143,164,202,258],"gives":[88],"notational":[90],"system":[91],"for":[92,283],"describing":[93],"complexity":[95],"sets":[98],"beyond":[99],"F":[100],"\u03c3":[101],"or":[102],"G":[103],"\u03b4":[104],"\u201cuniverse\u201d":[107],"refers":[108,116],"totality":[111,127],"all":[113],"\u201cForcing\u201d":[115],"Paul":[118],"Cohen's":[119],"technique":[120],"for,":[121],"sense,":[124],"changing":[125],"introduction":[130],"new":[132],"Here":[134],"\u201csmall\u201d":[135],"means":[136],"relatively":[137],"cardinality.":[139],"size":[141],"roughly":[148],"ath":[150],"iteration":[151],"power":[154],"operation.":[156],"Just":[157],"get":[159],"idea":[161],"what":[163],"theorem":[165],"might":[166],"saying,":[168],"we":[169,206,239,275],"argue":[171],"under":[173],"conditions,":[175],"closed":[178],"forcing,":[184],"exists":[187],"already.":[188],"There":[189],"are":[190],"number":[192],"other":[194],"qualifications":[195],"need":[197],"made":[200,221],"rough":[203],"description,":[204],"come":[208],"them":[210],"later.":[211],"Unlike,":[212],"say,":[213],"Shoenfield":[214],"absoluteness,":[215],"only":[219],"understood":[222],"terminology":[225],"forcing.":[227],"Since":[228],"typically":[231],"associated":[232],"with":[233],"pursuit":[235],"could":[240],"easily":[241],"assume":[242],"work":[245],"has":[246],"little":[247],"relevance":[248],"positive":[251],"However,":[257],"would":[259],"untrue.":[261],"Using":[262],"abstract":[263],"indirect":[265],"metamathematical":[266],"arguments,":[267],"availing":[269],"ourselves":[270],"principle,":[274],"prove":[277],"string":[279],"ZFC":[281],"which":[284],"no":[285],"direct":[286],"proof":[287],"known.":[289]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}