{"id":"https://openalex.org/W1973632985","doi":"https://doi.org/10.2307/2695026","title":"Slim models of Zermelo set theory","display_name":"Slim models of Zermelo set theory","publication_year":2001,"publication_date":"2001-06-01","ids":{"openalex":"https://openalex.org/W1973632985","doi":"https://doi.org/10.2307/2695026","mag":"1973632985"},"language":"en","primary_location":{"id":"doi:10.2307/2695026","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2695026","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/A5114010753","display_name":"A. R. D. Mathias","orcid":null},"institutions":[{"id":"https://openalex.org/I24715933","display_name":"University of Reunion Island","ror":"https://ror.org/005ypkf75","country_code":"RE","type":"education","lineage":["https://openalex.org/I24715933"]}],"countries":["RE"],"is_corresponding":true,"raw_author_name":"A. R. D. Mathias","raw_affiliation_strings":["D\u00e9partment de Math\u00e9matiques et Informatique, Universit\u00e9 de la R\u00e9union, BP 7151, F97715 Saint Denis de la R\u00e9union, Messageries Cedex 9, FranceOutre-Mer, E-mail:","Universit\u00e9 de La R\u00e9union"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partment de Math\u00e9matiques et Informatique, Universit\u00e9 de la R\u00e9union, BP 7151, F97715 Saint Denis de la R\u00e9union, Messageries Cedex 9, FranceOutre-Mer, E-mail:","institution_ids":["https://openalex.org/I24715933"]},{"raw_affiliation_string":"Universit\u00e9 de La R\u00e9union","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5114010753"],"corresponding_institution_ids":["https://openalex.org/I24715933"],"apc_list":null,"apc_paid":null,"fwci":14.5123,"has_fulltext":false,"cited_by_count":96,"citation_normalized_percentile":{"value":0.99525112,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"66","issue":"2","first_page":"487","last_page":"496"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9975000023841858,"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":0.9975000023841858,"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":0.958299994468689,"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/T11567","display_name":"semigroups and automata theory","score":0.9528999924659729,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8169752359390259},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6723980903625488},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6484787464141846},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.5832198262214661},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5557630062103271},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.555729329586029},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5413375496864319},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44928526878356934},{"id":"https://openalex.org/keywords/universal-set","display_name":"Universal set","score":0.4470311999320984},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.42320147156715393},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3501657247543335},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33504098653793335},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.27912023663520813},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1505277454853058},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12117764353752136},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0969034731388092}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8169752359390259},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6723980903625488},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6484787464141846},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.5832198262214661},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5557630062103271},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.555729329586029},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5413375496864319},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44928526878356934},{"id":"https://openalex.org/C102565666","wikidata":"https://www.wikidata.org/wiki/Q1378301","display_name":"Universal set","level":3,"score":0.4470311999320984},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.42320147156715393},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3501657247543335},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33504098653793335},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.27912023663520813},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1505277454853058},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12117764353752136},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0969034731388092},{"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2307/2695026","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2695026","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.28.1640","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.1640","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.univ-reunion.fr/~ardm/slim.ps","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183746455","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183746455","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1492647052","https://openalex.org/W2007983321","https://openalex.org/W2022273650","https://openalex.org/W2060319527","https://openalex.org/W2079713831","https://openalex.org/W2079743999","https://openalex.org/W2091425612","https://openalex.org/W2551720480","https://openalex.org/W4244876544","https://openalex.org/W7008280860"],"related_works":["https://openalex.org/W1574825745","https://openalex.org/W4229841181","https://openalex.org/W2067638726","https://openalex.org/W2500725777","https://openalex.org/W2957475467","https://openalex.org/W2079743999","https://openalex.org/W1831162581","https://openalex.org/W1516439450","https://openalex.org/W2504990261","https://openalex.org/W102647493"],"abstract_inverted_index":{"Abstract":[0],"Working":[1],"in":[2,26,81],"Z":[3],"+":[4],"KP":[5],",":[6],"we":[7],"give":[8],"a":[9,24,41,45,57,72,90,94],"new":[10],"proof":[11],"that":[12,48],"the":[13,31],"class":[14],"of":[15,37,76],"hereditarily":[16],"finite":[17],"sets":[18],"cannot":[19],"be":[20,23],"proved":[21],"to":[22,33],"set":[25,28],"Zermelo":[27,77],"theory,":[29],"extend":[30],"method":[32],"establish":[34],"other":[35],"failures":[36],"replacement,":[38],"and":[39],"exhibit":[40],"formula":[42],"\u03a6(":[43,92],"\u03bb,":[44,93],")":[46],"such":[47],"for":[49,61,83],"any":[50],"sequence":[51],"\u27e8":[52],"A":[53,65,86],"\u03bb":[54,56,63,66,68,85,87],"\u2223":[55,91],"limit":[58],"ordinal\u27e9":[59],"where":[60],"each":[62],".":[64],"\u2286":[67],"2,":[69],"there":[70],"is":[71],"supertransitive":[73],"inner":[74],"model":[75],"containing":[78],"all":[79],"ordinals":[80],"which":[82],"every":[84],"=":[88],"{":[89],")}.":[95]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":14},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}