{"id":"https://openalex.org/W2126219331","doi":"https://doi.org/10.2307/2275247","title":"Consequences of arithmetic for set theory","display_name":"Consequences of arithmetic for set theory","publication_year":1994,"publication_date":"1994-03-01","ids":{"openalex":"https://openalex.org/W2126219331","doi":"https://doi.org/10.2307/2275247","mag":"2126219331"},"language":"en","primary_location":{"id":"doi:10.2307/2275247","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2275247","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/6E2165299E1461C9659B6AEC46D1953F/S002248120002020Xa.pdf/div-class-title-consequences-of-arithmetic-for-set-theory-div.pdf","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":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/6E2165299E1461C9659B6AEC46D1953F/S002248120002020Xa.pdf/div-class-title-consequences-of-arithmetic-for-set-theory-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006815009","display_name":"Lorenz Halbe\u0131sen","orcid":"https://orcid.org/0000-0001-6078-7237"},"institutions":[{"id":"https://openalex.org/I2799323385","display_name":"Board of the Swiss Federal Institutes of Technology","ror":"https://ror.org/01rvn4p91","country_code":"CH","type":"government","lineage":["https://openalex.org/I2799323385"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Lorenz Halbeisen","raw_affiliation_strings":["Department of Mathematics, Eldgen. Technische Hochschule, Z\u00fcrich, Switzerland, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Eldgen. Technische Hochschule, Z\u00fcrich, Switzerland, E-mail:","institution_ids":["https://openalex.org/I2799323385"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024923217","display_name":"Saharon Shelah","orcid":"https://orcid.org/0000-0003-0462-3152"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Saharon Shelah","raw_affiliation_strings":["Institute of Mathematics, Hebrew University Jerusalem, Jerusalem., Israel, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Hebrew University Jerusalem, Jerusalem., Israel, E-mail:","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":36,"citation_normalized_percentile":{"value":0.24105572,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"59","issue":"1","first_page":"30","last_page":"40"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9980999827384949,"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":0.9980999827384949,"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":0.9908999800682068,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.8359189629554749},{"id":"https://openalex.org/keywords/power-set","display_name":"Power set","score":0.7892802953720093},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7248845100402832},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.6995585560798645},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.66725754737854},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6432275176048279},{"id":"https://openalex.org/keywords/cardinal-number","display_name":"Cardinal number (linguistics)","score":0.5658618211746216},{"id":"https://openalex.org/keywords/set-function","display_name":"Set function","score":0.5631381869316101},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.556486189365387},{"id":"https://openalex.org/keywords/universal-set","display_name":"Universal set","score":0.5036644339561462},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.49689510464668274},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4962649941444397},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4713565707206726},{"id":"https://openalex.org/keywords/infinite-set","display_name":"Infinite set","score":0.4556979238986969},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.42395636439323425},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.135349303483963}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.8359189629554749},{"id":"https://openalex.org/C100643331","wikidata":"https://www.wikidata.org/wiki/Q205170","display_name":"Power set","level":3,"score":0.7892802953720093},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7248845100402832},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.6995585560798645},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.66725754737854},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6432275176048279},{"id":"https://openalex.org/C2778408900","wikidata":"https://www.wikidata.org/wiki/Q1329258","display_name":"Cardinal number (linguistics)","level":2,"score":0.5658618211746216},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.5631381869316101},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.556486189365387},{"id":"https://openalex.org/C102565666","wikidata":"https://www.wikidata.org/wiki/Q1378301","display_name":"Universal set","level":3,"score":0.5036644339561462},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.49689510464668274},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4962649941444397},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4713565707206726},{"id":"https://openalex.org/C199879729","wikidata":"https://www.wikidata.org/wiki/Q205140","display_name":"Infinite set","level":3,"score":0.4556979238986969},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.42395636439323425},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.135349303483963},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2275247","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2275247","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/6E2165299E1461C9659B6AEC46D1953F/S002248120002020Xa.pdf/div-class-title-consequences-of-arithmetic-for-set-theory-div.pdf","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":{"id":"doi:10.2307/2275247","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2275247","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/6E2165299E1461C9659B6AEC46D1953F/S002248120002020Xa.pdf/div-class-title-consequences-of-arithmetic-for-set-theory-div.pdf","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2126219331.pdf","grobid_xml":"https://content.openalex.org/works/W2126219331.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1541012876","https://openalex.org/W1983910091","https://openalex.org/W1997237005","https://openalex.org/W2001852972","https://openalex.org/W2028322461","https://openalex.org/W2066268301","https://openalex.org/W4233741736"],"related_works":["https://openalex.org/W3194235253","https://openalex.org/W2098788035","https://openalex.org/W4388295869","https://openalex.org/W177504871","https://openalex.org/W2378801550","https://openalex.org/W2126219331","https://openalex.org/W2553290232","https://openalex.org/W4237730467","https://openalex.org/W3021560513","https://openalex.org/W2477201441"],"abstract_inverted_index":{"Abstract":[0],"In":[1,18],"this":[2,37,73,100,121],"paper,":[3],"we":[4,118],"consider":[5,48],"certain":[6],"cardinals":[7,26,93],"in":[8,35,94,131],"ZF":[9,36,104,132],"(set":[10,20],"theory":[11,21],"without":[12,61],"AC,":[13],"the":[14,54,70,78,81,123,149],"axiom":[15],"of":[16,56,59,72,80,84,99,157],"choice).":[17],"ZFC":[19],"with":[22,171],"AC),":[23],"given":[24,44],"any":[25],"and":[27,117],",":[28],"either":[29],"\u2264":[30,32],"or":[31],".":[33,86],"However,":[34],"is":[38,88,102,122,129,136,169],"no":[39],"longer":[40],"so.":[41],"For":[42],"a":[43,158],"infinite":[45,138,153],"set":[46,55,83,154],"A":[47,52,60,68,85,107,112],"seq":[49,109],"1-1":[50,66,110],"(":[51,67,111,166],"),":[53],"all":[57],"sequences":[58],"repetition.":[62],"We":[63],"compare":[64],"|seq":[65],")|,":[69],"cardinality":[71,79],"set,":[74,139],"to":[75],"|":[76,115,141,144,146],"|,":[77],"power":[82],"What":[87],"provable":[89,130],"about":[90],"these":[91],"two":[92],"ZF?":[95],"The":[96],"main":[97],"result":[98],"paper":[101],"that":[103,120,133],"\u22a2":[105],"\u2200":[106],"(|":[108],")|":[113],"\u2260":[114],"|),":[116],"show":[119],"best":[124],"possible":[125],"result.":[126],"Furthermore,":[127],"it":[128],"if":[134],"B":[135,155,163,167],"an":[137],"then":[140],"fin(B)|":[142],"&lt;":[143],"(B*)":[145],"even":[147],"though":[148],"existence":[150],"for":[151],"some":[152],"*":[156],"function":[159],"\u0192":[160],"from":[161],"fin(":[162],"*)":[164,168],"onto":[165],"consistent":[170],"ZF.":[172]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
