{"id":"https://openalex.org/W2088815887","doi":"https://doi.org/10.2307/2273669","title":"Blunt and topless end extensions of models of set theory","display_name":"Blunt and topless end extensions of models of set theory","publication_year":1983,"publication_date":"1983-12-01","ids":{"openalex":"https://openalex.org/W2088815887","doi":"https://doi.org/10.2307/2273669","mag":"2088815887"},"language":"en","primary_location":{"id":"doi:10.2307/2273669","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273669","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/A5004178046","display_name":"Matt Kaufmann","orcid":"https://orcid.org/0009-0004-5667-4888"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matt Kaufmann","raw_affiliation_strings":["Purdue University, West Lafayette, Indiana 47907"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Purdue University, West Lafayette, Indiana 47907","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004178046"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":2.7648,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.90776226,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"48","issue":"4","first_page":"1053","last_page":"1073"},"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":0.9681000113487244,"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/T13966","display_name":"Neurological and metabolic disorders","score":0.9459999799728394,"subfield":{"id":"https://openalex.org/subfields/2712","display_name":"Endocrinology, Diabetes and Metabolism"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cofinality","display_name":"Cofinality","score":0.8222348690032959},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.8141926527023315},{"id":"https://openalex.org/keywords/uncountable-set","display_name":"Uncountable set","score":0.7903323173522949},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6566417217254639},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5278563499450684},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5035561919212341},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4695858359336853},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.43017399311065674},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2878970503807068},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.07507491111755371},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07376417517662048},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06043952703475952},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.052991628646850586}],"concepts":[{"id":"https://openalex.org/C148070024","wikidata":"https://www.wikidata.org/wiki/Q1283623","display_name":"Cofinality","level":4,"score":0.8222348690032959},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.8141926527023315},{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.7903323173522949},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6566417217254639},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5278563499450684},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5035561919212341},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4695858359336853},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.43017399311065674},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2878970503807068},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.07507491111755371},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07376417517662048},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06043952703475952},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.052991628646850586},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273669","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273669","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:CULeuclid:euclid.jsl/1183741414","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183741414","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":[{"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth","score":0.5400000214576721}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W40029885","https://openalex.org/W986162294","https://openalex.org/W1008748165","https://openalex.org/W1898322248","https://openalex.org/W1976365164","https://openalex.org/W1977994335","https://openalex.org/W2036283644","https://openalex.org/W2048854384","https://openalex.org/W2061250638","https://openalex.org/W2070815955","https://openalex.org/W2091476429","https://openalex.org/W2969873114","https://openalex.org/W4293117209"],"related_works":["https://openalex.org/W2087618015","https://openalex.org/W2103474290","https://openalex.org/W2052469854","https://openalex.org/W1978298715","https://openalex.org/W2088815887","https://openalex.org/W2157535554","https://openalex.org/W1551473042","https://openalex.org/W2955857277","https://openalex.org/W1607154110","https://openalex.org/W4288296004"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"be":[2,130],"a":[3,18,39,71,83,91,98,136,142,165,173,182,196,246,283,303,332],"well-founded":[4,72,99,192,349],"model":[5,40,73,299,325],"of":[6,10,74,141,144,169,178,188,191,240,266,285,295,300,315,326,328,342,351],"ZFC":[7,241,267,301,327],"whose":[8],"class":[9,190],"ordinals":[11,105],"has":[12,17,42,78,82,90,156,302,331],"uncountable":[13,79,352],"cofinality,":[14],"such":[15,38,76],"that":[16,35,77,159,170,323,347],"\u03a3":[19,85,197,247,271],"n":[20,25,198,203,248,253],"end":[21,45,55,87,94,101,199,249,260,273,305,335,363,370],"extension":[22,95,200,250,274,306],"for":[23,65,118,201,228,251,348,355],"each":[24,202],"\u2208":[26,204,254],"\u03c9":[27,205,211,236,255,262],".":[28,153,206],"It":[29],"is":[30,37,70,139,176,213,226,289],"shown":[31],"in":[32,217,277,292],"Theorem":[33,67,224,278,296,311],"1.1":[34,225],"there":[36],"which":[41,106,127,194,244,268,288,307,345],"no":[43,59,258,270],"elementary":[44,93,100,259,334],"extension.":[46,261,336],"In":[47,112,231],"the":[48,147,189,220,293,340,343],"process":[49],"some":[50],"interesting":[51],"facts":[52],"about":[53],"topless":[54,84,92,333,362],"extensions":[56,364],"(those":[57],"with":[58,339,359],"least":[60],"new":[61],"ordinal)":[62],"are":[63,107,116,242,275,365],"uncovered,":[64],"example":[66],"2.1:":[68],"If":[69],"ZFC,":[75],"cofinality":[80,330,353],"and":[81,96,103,186,234,317,319,354],"3":[86,272],"extension,":[88,102],"then":[89],"also":[97,290],"contains":[104],"(in":[108],")":[109],"highly":[110],"hyperinaccessible.":[111],"\u00a73":[113],"related":[114],"results":[115,314],"proved":[117],"\u03ba":[119,123,150,209,356,360],"-like":[120,238,264,357],"models":[121,193,239,265,350,358],"(":[122],"any":[124],"regular":[125],"cardinal)":[126],"need":[128],"not":[129],"well":[131],"founded.":[132],"As":[133],"an":[134],"application":[135],"soft":[137],"proof":[138,168,175,281,294],"given":[140,177],"theorem":[143],"Schmerl":[145],"on":[146],"model-theoretic":[148],"relation":[149],"\u2192":[151],"\u03bb":[152],"(The":[154],"author":[155],"been":[157],"informed":[158],"Silver":[160,187],"had":[161],"earlier,":[162],"independently,":[163],"found":[164],"similar":[166],"unpublished":[167],"theorem.)":[171],"Also,":[172],"simpler":[174],"(a":[179],"generalization":[180],"of)":[181],"characterization":[183],"by":[184,223,321],"Keisler":[185,316],"have":[195,245,257,269],"The":[207,280],"case":[208],"=":[210],"1":[212,237,263],"investigated":[214],"more":[215],"deeply":[216],"\u00a74,":[218],"where":[219],"problem":[221],"solved":[222],"considered":[227],"non-well-founded":[229],"models.":[230],"Theorems":[232],"4.1":[233],"4.4,":[235],"constructed":[243],"all":[252],"but":[256],"produced":[276],"4.2.":[279],"uses":[282],"notion":[284],"satisfaction":[286],"class,":[287],"applied":[291],"4.6:":[297],"No":[298],"definable":[304],"satisfies":[308],"ZFC.":[309],"Finally,":[310],"5.1":[312],"generalizes":[313],"Morley,":[318],"Hutchinson,":[320],"asserting":[322],"every":[324],"countable":[329],"This":[337],"contrasts":[338],"rest":[341],"paper,":[344],"shows":[346],"regular,":[361],"much":[366],"rarer":[367],"than":[368],"blunt":[369],"extensions.":[371]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}