{"id":"https://openalex.org/W2806153888","doi":"https://doi.org/10.1017/s1755020320000143","title":"DEPENDENT CHOICE, PROPERNESS, AND GENERIC ABSOLUTENESS","display_name":"DEPENDENT CHOICE, PROPERNESS, AND GENERIC ABSOLUTENESS","publication_year":2020,"publication_date":"2020-07-02","ids":{"openalex":"https://openalex.org/W2806153888","doi":"https://doi.org/10.1017/s1755020320000143","mag":"2806153888"},"language":"en","primary_location":{"id":"doi:10.1017/s1755020320000143","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020320000143","pdf_url":null,"source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"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 Review of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1806.04077","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017293866","display_name":"David Asper\u00f3","orcid":"https://orcid.org/0000-0002-7972-2860"},"institutions":[{"id":"https://openalex.org/I1118541","display_name":"University of East Anglia","ror":"https://ror.org/026k5mg93","country_code":"GB","type":"education","lineage":["https://openalex.org/I1118541"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"DAVID ASPER\u00d3","raw_affiliation_strings":["SCHOOL OF MATHEMATICS UNIVERSITY OF EAST ANGLIA NORWICH NR4 7TJ, UK E-mail:","(University of East Anglia, Norwich"],"affiliations":[{"raw_affiliation_string":"SCHOOL OF MATHEMATICS UNIVERSITY OF EAST ANGLIA NORWICH NR4 7TJ, UK E-mail:","institution_ids":["https://openalex.org/I1118541"]},{"raw_affiliation_string":"(University of East Anglia, Norwich","institution_ids":["https://openalex.org/I1118541"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086246827","display_name":"Asaf Karagila","orcid":"https://orcid.org/0000-0003-1289-0904"},"institutions":[{"id":"https://openalex.org/I1118541","display_name":"University of East Anglia","ror":"https://ror.org/026k5mg93","country_code":"GB","type":"education","lineage":["https://openalex.org/I1118541"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"ASAF KARAGILA","raw_affiliation_strings":["SCHOOL OF MATHEMATICS UNIVERSITY OF EAST ANGLIA NORWICH NR4 7TJ, UK E-mail:","(University of East Anglia, Norwich"],"affiliations":[{"raw_affiliation_string":"SCHOOL OF MATHEMATICS UNIVERSITY OF EAST ANGLIA NORWICH NR4 7TJ, UK E-mail:","institution_ids":["https://openalex.org/I1118541"]},{"raw_affiliation_string":"(University of East Anglia, Norwich","institution_ids":["https://openalex.org/I1118541"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017293866"],"corresponding_institution_ids":["https://openalex.org/I1118541"],"apc_list":null,"apc_paid":null,"fwci":1.9344,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.83854525,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"14","issue":"1","first_page":"225","last_page":"249"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9926000237464905,"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":0.9722999930381775,"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/absoluteness","display_name":"Absoluteness","score":0.9919995665550232},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.8399823904037476},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.6975525617599487},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6927163004875183},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6543157696723938},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.5984190106391907},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.5783563256263733},{"id":"https://openalex.org/keywords/constructive-set-theory","display_name":"Constructive set theory","score":0.5073065161705017},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.49513188004493713},{"id":"https://openalex.org/keywords/axiom-independence","display_name":"Axiom independence","score":0.4624491035938263},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.43323221802711487},{"id":"https://openalex.org/keywords/foundation","display_name":"Foundation (evidence)","score":0.43039023876190186},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.38711458444595337},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3682355284690857},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3436765968799591},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.23874583840370178},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20750626921653748},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10464400053024292},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.08776286244392395},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.0751316249370575},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06492370367050171}],"concepts":[{"id":"https://openalex.org/C2780102774","wikidata":"https://www.wikidata.org/wiki/Q4669873","display_name":"Absoluteness","level":2,"score":0.9919995665550232},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.8399823904037476},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.6975525617599487},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6927163004875183},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6543157696723938},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.5984190106391907},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.5783563256263733},{"id":"https://openalex.org/C556429856","wikidata":"https://www.wikidata.org/wiki/Q5164501","display_name":"Constructive set theory","level":5,"score":0.5073065161705017},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.49513188004493713},{"id":"https://openalex.org/C170088968","wikidata":"https://www.wikidata.org/wiki/Q4830547","display_name":"Axiom independence","level":3,"score":0.4624491035938263},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.43323221802711487},{"id":"https://openalex.org/C2780966255","wikidata":"https://www.wikidata.org/wiki/Q5474306","display_name":"Foundation (evidence)","level":2,"score":0.43039023876190186},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.38711458444595337},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3682355284690857},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3436765968799591},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.23874583840370178},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20750626921653748},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10464400053024292},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.08776286244392395},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0751316249370575},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06492370367050171},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"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/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s1755020320000143","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020320000143","pdf_url":null,"source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"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 Review of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1806.04077","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.04077","pdf_url":"https://arxiv.org/pdf/1806.04077","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:ueaeprints.uea.ac.uk:74693","is_oa":true,"landing_page_url":null,"pdf_url":"https://ueaeprints.uea.ac.uk/id/eprint/74693/1/ac_pfa_and_chang.pdf","source":{"id":"https://openalex.org/S4306400384","display_name":"UEA Digital Repository (University of East Anglia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1118541","host_organization_name":"University of East Anglia","host_organization_lineage":["https://openalex.org/I1118541"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1806.04077","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.04077","pdf_url":"https://arxiv.org/pdf/1806.04077","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1717991059","display_name":null,"funder_award_id":"EP/N032160/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3728093668","display_name":"Isaac Newton Institute for Mathematical Sciences","funder_award_id":"EP/K032208/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4421442999","display_name":null,"funder_award_id":"EP/K032208","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4984718776","display_name":null,"funder_award_id":"P/K032208/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5128091834","display_name":null,"funder_award_id":"EP/K032208/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7000731051","display_name":null,"funder_award_id":"EP/K032208/1","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G8755151645","display_name":"Iterated forcing with side conditions and high forcing axioms","funder_award_id":"EP/N032160/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W187570007","https://openalex.org/W1540715591","https://openalex.org/W1541012876","https://openalex.org/W1594319355","https://openalex.org/W1595388840","https://openalex.org/W1598405987","https://openalex.org/W1608084331","https://openalex.org/W1969555173","https://openalex.org/W1981694349","https://openalex.org/W1996087038","https://openalex.org/W2020754577","https://openalex.org/W2045975809","https://openalex.org/W2048236519","https://openalex.org/W2069506349","https://openalex.org/W2073171092","https://openalex.org/W2094042091","https://openalex.org/W2119265237","https://openalex.org/W2130670935","https://openalex.org/W2143005794","https://openalex.org/W2157996049","https://openalex.org/W2315572811","https://openalex.org/W2604352492","https://openalex.org/W2609109703","https://openalex.org/W2755219037","https://openalex.org/W2799703541","https://openalex.org/W2803798297","https://openalex.org/W2940894182","https://openalex.org/W2962887510","https://openalex.org/W3098134592","https://openalex.org/W3099875334","https://openalex.org/W3100820666","https://openalex.org/W3103011296","https://openalex.org/W3104040049","https://openalex.org/W3174037810","https://openalex.org/W4210783718","https://openalex.org/W4243701117","https://openalex.org/W6662283228","https://openalex.org/W6785187067"],"related_works":["https://openalex.org/W1995120876","https://openalex.org/W2796622564","https://openalex.org/W288388583","https://openalex.org/W284553743","https://openalex.org/W2017671599","https://openalex.org/W2980408391","https://openalex.org/W2060433450","https://openalex.org/W3197691547","https://openalex.org/W2102114482","https://openalex.org/W4230409512"],"abstract_inverted_index":{"Abstract":[0],"We":[1,84],"show":[2],"that":[3],"Dependent":[4],"Choice":[5],"is":[6,61],"a":[7,101,130,134,151,155],"sufficient":[8],"choice":[9],"principle":[10],"for":[11,20,24,56,133,154],"developing":[12,57],"the":[13,25,29,53,63,75,79,91,105,109,144],"basic":[14,88],"theory":[15,66,148],"of":[16,31,43,81,90,108,137,146,158],"proper":[17],"forcing,":[18],"and":[19,99,117,140],"deriving":[21],"generic":[22,106],"absoluteness":[23,107],"Chang":[26],"model":[27],"in":[28,72,78,95,113],"presence":[30,80],"large":[32,82,156],"cardinals,":[33],"even":[34],"with":[35],"respect":[36],"to":[37,69,143],"$\\mathsf":[38,47,96,114,118,124],"{DC}$":[39,49,116,128],"-preserving":[40],"symmetric":[41],"submodels":[42],"forcing":[44],"extensions.":[45],"Hence,":[46],"{ZF}+\\mathsf":[48,115],"not":[50],"only":[51],"provides":[52],"right":[54,64],"framework":[55],"classical":[58],"analysis,":[59],"but":[60],"also":[62,85,150],"base":[65],"over":[67],"which":[68],"safeguard":[70],"truth":[71],"analysis":[73],"from":[74],"independence":[76],"phenomenon":[77],"cardinals.":[83],"investigate":[86],"some":[87],"consequences":[89],"Proper":[92,110],"Forcing":[93,111],"Axiom":[94,112],"{ZF}$":[97],",":[98],"formulate":[100],"natural":[102,131,152],"question":[103],"about":[104],"{ZFC}$":[119],".":[120],"Our":[121],"results":[122],"confirm":[123],"{ZF}":[125],"+":[126],"\\mathsf":[127],"as":[129],"foundation":[132,153],"significant":[135],"portion":[136],"\u201cclassical":[138],"mathematics\u201d":[139],"provide":[141],"support":[142],"idea":[145],"this":[147],"being":[149],"part":[157],"set":[159],"theory.":[160]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2018-06-13T00:00:00"}