{"id":"https://openalex.org/W2019760148","doi":"https://doi.org/10.1002/malq.200310080","title":"The cumulative hierarchy and the constructible universe of ZFA","display_name":"The cumulative hierarchy and the constructible universe of ZFA","publication_year":2003,"publication_date":"2003-11-26","ids":{"openalex":"https://openalex.org/W2019760148","doi":"https://doi.org/10.1002/malq.200310080","mag":"2019760148"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200310080","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200310080","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5109889444","display_name":"Matteo Viale","orcid":null},"institutions":[{"id":"https://openalex.org/I1330701686","display_name":"Collegio Carlo Alberto","ror":"https://ror.org/0397knh37","country_code":"IT","type":"education","lineage":["https://openalex.org/I1330701686"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Matteo Viale","raw_affiliation_strings":["Dipartimento di Matematica, Universita\u0300 di Torino, via Carlo Alberto 10, 10123 Torino, Italia","Dipartimento di Matematica, Universit\u00e1 di Torino, via Carlo Alberto 10, 10123 Torino, Italia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universita\u0300 di Torino, via Carlo Alberto 10, 10123 Torino, Italia","institution_ids":["https://openalex.org/I1330701686"]},{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e1 di Torino, via Carlo Alberto 10, 10123 Torino, Italia","institution_ids":["https://openalex.org/I1330701686"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109889444"],"corresponding_institution_ids":["https://openalex.org/I1330701686"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.36,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.60087577,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"50","issue":"1","first_page":"99","last_page":"103"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9621999859809875,"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"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9621999859809875,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9341999888420105,"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"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9136000275611877,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/mathematics","display_name":"Mathematics","score":0.7006742358207703},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6177155375480652},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.6090307831764221},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.6049476265907288},{"id":"https://openalex.org/keywords/universe","display_name":"Universe","score":0.5704447031021118},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.49483078718185425},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.42868974804878235},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40964511036872864},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39710134267807007},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16329863667488098},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14240393042564392},{"id":"https://openalex.org/keywords/astrophysics","display_name":"Astrophysics","score":0.07452163100242615}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7006742358207703},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6177155375480652},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6090307831764221},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.6049476265907288},{"id":"https://openalex.org/C84999194","wikidata":"https://www.wikidata.org/wiki/Q1","display_name":"Universe","level":2,"score":0.5704447031021118},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.49483078718185425},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.42868974804878235},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40964511036872864},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39710134267807007},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16329863667488098},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14240393042564392},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.07452163100242615},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.200310080","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200310080","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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":6,"referenced_works":["https://openalex.org/W138853701","https://openalex.org/W1814429312","https://openalex.org/W2462383671","https://openalex.org/W2970349335","https://openalex.org/W4250230991","https://openalex.org/W6638778330"],"related_works":["https://openalex.org/W587735977","https://openalex.org/W315394019","https://openalex.org/W1978142926","https://openalex.org/W2365264209","https://openalex.org/W3157395178","https://openalex.org/W4309585848","https://openalex.org/W2509431957","https://openalex.org/W2265383332","https://openalex.org/W1895405313","https://openalex.org/W2800754277"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"present":[2],"two":[3],"results":[4],"which":[5],"shed":[6],"some":[7],"more":[8],"light":[9],"on":[10],"the":[11,17,40,53,65,70,90,97,103,108,117,120],"deep":[12],"connection":[13],"between":[14],"ZFA":[15,43,101],"and":[16,31,61,119],"standard":[18,91,118],"ZF":[19],"set":[20],"theory:":[21],"First":[22],"of":[23,29,42,57,69,100,107,111],"all":[24],"we":[25,74],"refine":[26],"a":[27,58,82],"result":[28],"Forti":[30],"Honsell":[32],"(see":[33],"[5])":[34],"in":[35,87,93],"order":[36,94],"to":[37,50,80,89,95,116],"prove":[38],"that":[39,76],"universe":[41],"can":[44],"also":[45],"be":[46],"obtained":[47],"(without":[48],"appealing":[49],"choice)":[51],"as":[52,64,102],"least":[54,104],"fixed":[55,67,105],"point":[56,68,106],"continuous":[59,109],"operator":[60,110],"not":[62],"only":[63],"greatest":[66],"powerset":[71],"operator.":[72],"Next":[73],"show":[75],"it":[77],"is":[78],"possible":[79],"define":[81],"new":[83,121],"absolute":[84],"G\u00f6del":[85,112,122],"operation":[86],"addition":[88],"ones":[92],"obtain":[96],"\u201cconstructible\u201d":[98],"model":[99],"closure":[113],"with":[114],"respect":[115],"operations.":[123],"(\u00a9":[124],"2003":[125],"WILEY\u2010VCH":[126],"Verlag":[127],"GmbH":[128],"&amp;":[129],"Co.":[130],"KGaA,":[131],"Weinheim)":[132]},"counts_by_year":[{"year":2013,"cited_by_count":3}],"updated_date":"2026-07-07T14:30:12.667765","created_date":"2025-10-10T00:00:00"}
