{"id":"https://openalex.org/W2014768786","doi":"https://doi.org/10.1215/00294527-1960434","title":"Consecutive Singular Cardinals and the Continuum Function","display_name":"Consecutive Singular Cardinals and the Continuum Function","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2014768786","doi":"https://doi.org/10.1215/00294527-1960434","mag":"2014768786"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-1960434","is_oa":false,"landing_page_url":"https://doi.org/10.1215/00294527-1960434","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal 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/1112.1890","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066099291","display_name":"Arthur W. Apter","orcid":"https://orcid.org/0000-0002-7091-3628"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Arthur W. Apter","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5017436648","display_name":"Brent Cody","orcid":"https://orcid.org/0000-0001-5890-5222"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brent Cody","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066099291"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.08618211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"54","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998999834060669,"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":0.9998999834060669,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.991599977016449,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9879000186920166,"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":0.7119703888893127},{"id":"https://openalex.org/keywords/continuum-hypothesis","display_name":"Continuum hypothesis","score":0.6074255704879761},{"id":"https://openalex.org/keywords/singular-function","display_name":"Singular function","score":0.47386598587036133},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44376474618911743},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4217962622642517},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3628993034362793},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3493937849998474},{"id":"https://openalex.org/keywords/singular-integral","display_name":"Singular integral","score":0.1580847203731537},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.054638028144836426}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7119703888893127},{"id":"https://openalex.org/C96488702","wikidata":"https://www.wikidata.org/wiki/Q208416","display_name":"Continuum hypothesis","level":2,"score":0.6074255704879761},{"id":"https://openalex.org/C126578732","wikidata":"https://www.wikidata.org/wiki/Q2374166","display_name":"Singular function","level":4,"score":0.47386598587036133},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44376474618911743},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4217962622642517},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3628993034362793},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3493937849998474},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.1580847203731537},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.054638028144836426},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1215/00294527-1960434","is_oa":false,"landing_page_url":"https://doi.org/10.1215/00294527-1960434","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1112.1890","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1112.1890","pdf_url":"https://arxiv.org/pdf/1112.1890","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:CULeuclid:euclid.ndjfl/1361454970","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1361454970","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.639.1772","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.639.1772","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.people.vcu.edu/~bmcody/apco01.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.758.538","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.758.538","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1112.1890.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1112.1890","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1112.1890","pdf_url":"https://arxiv.org/pdf/1112.1890","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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W867212652","https://openalex.org/W1590233520","https://openalex.org/W1971801916","https://openalex.org/W1983867590","https://openalex.org/W1998865204","https://openalex.org/W2013447938","https://openalex.org/W2049932494","https://openalex.org/W2060319527","https://openalex.org/W2063833386","https://openalex.org/W2069773657","https://openalex.org/W2105223399","https://openalex.org/W2108458006","https://openalex.org/W2130670935","https://openalex.org/W2151715640","https://openalex.org/W2161613038","https://openalex.org/W2318231933","https://openalex.org/W3158438891","https://openalex.org/W3159730454","https://openalex.org/W4232672177"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2980963558","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W1976691234","https://openalex.org/W3212023493","https://openalex.org/W2090715877","https://openalex.org/W2014768786"],"abstract_inverted_index":{"We":[0,63],"show":[1,65],"that":[2,14,44,66],"from":[3],"a":[4,10,16,49,75,120,141],"supercompact":[5],"cardinal":[6],"\u03ba,":[7],"there":[8],"is":[9],"forcing":[11],"extension":[12],"V[G]":[13],"has":[15],"symmetric":[17],"inner":[18],"model":[19,47,76,142],"N":[20],"in":[21,41,79,122,140,152],"which":[22,80,123],"ZF+\u00acAC":[23],"holds,":[24],"\u03ba":[25,36,55,137],"and":[26,31,84,89,102,107,138],"\u03ba+":[27,139],"are":[28,86,104,160],"both":[29,87,105],"singular,":[30],"the":[32,42,45,67,90,108,126,149],"continuum":[33,91,109,150],"function":[34,92,110,151],"at":[35,93,111],"can":[37,70,95,113],"be":[38,71,96,114],"precisely":[39,97,115],"controlled,":[40,98],"sense":[43],"final":[46],"contains":[48],"sequence":[50],"of":[51,54,56,77,128,130,133,143,154],"distinct":[52,131],"subsets":[53,132],"length":[57],"equal":[58],"to":[59,73],"any":[60],"predetermined":[61],"ordinal.":[62],"also":[64],"above":[68],"situation":[69],"collapsed":[72],"obtain":[74],"ZF+\u00acAC\u03c9":[78],"either":[81],"(1)":[82],"\u21351":[83,94],"\u21352":[85],"singular":[88,106,135,158],"or":[99],"(2)":[100],"\u2135\u03c9":[101,112],"\u2135\u03c9+1":[103],"controlled.":[116],"Additionally,":[117],"we":[118,124],"discuss":[119],"result":[121],"separate":[125],"lengths":[127],"sequences":[129],"consecutive":[134,157],"cardinals":[136,159],"ZF.":[144],"Some":[145],"open":[146],"questions":[147],"concerning":[148],"models":[153],"ZF":[155],"with":[156],"posed.":[161]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}