{"id":"https://openalex.org/W1562375003","doi":"https://doi.org/10.2307/2586536","title":"On inverse \u03b3-systems and the number of<i>L</i><sub>\u221e\u03bb</sub>-equivalent, non-isomorphic models for \u03bb singular","display_name":"On inverse \u03b3-systems and the number of<i>L</i><sub>\u221e\u03bb</sub>-equivalent, non-isomorphic models for \u03bb singular","publication_year":2000,"publication_date":"2000-03-01","ids":{"openalex":"https://openalex.org/W1562375003","doi":"https://doi.org/10.2307/2586536","mag":"1562375003"},"language":"en","primary_location":{"id":"doi:10.2307/2586536","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586536","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/A5024923217","display_name":"Saharon Shelah","orcid":"https://orcid.org/0000-0003-0462-3152"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]},{"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","US"],"is_corresponding":false,"raw_author_name":"Saharon Shelah","raw_affiliation_strings":["Institute of Mathematics, The Hebrew University, Jerusalem, Israel","Rutgers University, Hill Ctr-Busch, New Brunswick, New Jersey 08903, USA, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, The Hebrew University, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"Rutgers University, Hill Ctr-Busch, New Brunswick, New Jersey 08903, USA, E-mail:","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043942259","display_name":"Pauli V\u00e4is\u00e4nen","orcid":null},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Pauli V\u00e4is\u00e4nen","raw_affiliation_strings":["Department of Mathematics, P. O. Box 4, 00014, University of Helsinki, Finland, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, P. O. Box 4, 00014, University of Helsinki, Finland, E-mail:","institution_ids":["https://openalex.org/I133731052"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.07782369,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"1","first_page":"272","last_page":"284"},"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9959999918937683,"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"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9914000034332275,"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":0.8936907052993774},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8830444812774658},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.8016833066940308},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.683582067489624},{"id":"https://openalex.org/keywords/uncountable-set","display_name":"Uncountable set","score":0.6674326658248901},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48873066902160645},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4839613735675812},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.46445322036743164},{"id":"https://openalex.org/keywords/cofinality","display_name":"Cofinality","score":0.413728803396225},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.058384597301483154},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.055520445108413696}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.8936907052993774},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8830444812774658},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.8016833066940308},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.683582067489624},{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.6674326658248901},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48873066902160645},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4839613735675812},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.46445322036743164},{"id":"https://openalex.org/C148070024","wikidata":"https://www.wikidata.org/wiki/Q1283623","display_name":"Cofinality","level":4,"score":0.413728803396225},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.058384597301483154},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.055520445108413696},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","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/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2586536","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586536","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","score":0.5600000023841858,"display_name":"Decent work and economic growth"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W128909481","https://openalex.org/W616212347","https://openalex.org/W1542735529","https://openalex.org/W1964601319","https://openalex.org/W2020372741","https://openalex.org/W2074658194","https://openalex.org/W2084831008","https://openalex.org/W2319390012","https://openalex.org/W2498536233","https://openalex.org/W2531760221","https://openalex.org/W2971268466","https://openalex.org/W4388284830"],"related_works":["https://openalex.org/W2103474290","https://openalex.org/W2973517705","https://openalex.org/W4288278828","https://openalex.org/W2965212342","https://openalex.org/W2949179291","https://openalex.org/W4301266944","https://openalex.org/W2140984628","https://openalex.org/W2599341819","https://openalex.org/W2005025079","https://openalex.org/W1978298715"],"abstract_inverted_index":{"Abstract":[0],"Suppose":[1],"\u03bb":[2,30,120,148,167,178,182,191,207,220,235,240,245,267,274,277],"is":[3,127,140,185,210,268],"a":[4,12,102,141,186],"singular":[5],"cardinal":[6,69],"of":[7,14,23,26,28,44,51,79,111,131,189,214,259],"uncountable":[8],"cofinality":[9],"\u03ba.":[10],"For":[11],"model":[13,142,187],"cardinality":[15,29,83,135,190,218],"\u03bb,":[16,137],"let":[17],"No(":[18,150,193,264],")":[19,146,151,194,265],"denote":[20],"the":[21,114,230,251,256,262],"number":[22],"isomorphism":[24],"types":[25],"models":[27],"which":[31],"are":[32],"L":[33],"\u221e\u03bb":[34],"-equivalent":[35],"to":[36],".":[37],"In":[38,58,197],"[7]":[39],"Shelah":[40,60,100],"considered":[41],"inverse":[42,74,106,129,212],"\u03ba-systems":[43,107],"abelian":[45,80,132,215],"groups":[46,81,133,216],"and":[47,88,108,149,236],"their":[48],"certain":[49],"kind":[50],"quotient":[52],"limits":[53],"Gr(":[54],")/":[55,90,154,224],"Fact(":[56,91,155,225],").":[57],"particular":[59],"proved":[61],"in":[62,96],"[7,":[63],"Fact":[64],"3.10]":[65],"that":[66,77,116,144,222],"for":[67,121,168,173,202,241,275],"every":[68,122,169,174,203,276],"\u039c":[70,86,176,180,205,228,247],"there":[71,139,184,209],"exists":[72],"an":[73,128,160,211],"\u03ba-system":[75,130,213],"such":[76,143,221],"consists":[78],"having":[82,134,217],"at":[84],"most":[85],"\u03ba":[87,118,165,183,208,233,272],"card(Gr(":[89,153,223],"))":[92,226],"=":[93,147,152,181,195,227,266],"\u039c.":[94,196],"Later":[95],"[8,":[97],"Theorem":[98],"3.3]":[99],"showed":[101],"strict":[103],"connection":[104],"between":[105],"possible":[109,257,269],"values":[110],"No":[112],"(under":[113,229],"assumption":[115],"\u03b8":[117,123,164,170,237,243,271],"&lt;":[119,124,136,166,171,177,219,234,239,244,278],"\u03bb):":[125,172],"if":[126],"then":[138],"card(":[145],")).":[156],"The":[157],"following":[158],"was":[159],"immediate":[161],"consequence":[162,254],"(when":[163],"nonzero":[175,204],"or":[179],",":[188],"with":[192,250],"this":[198],"paper":[199],"we":[200],"show:":[201],"\u2264":[206],"assumptions":[231],"2":[232],"&lt;\u03ba":[238],"all":[242],"when":[246,270],"&gt;":[248,273],"\u03bb),":[249],"obvious":[252],"new":[253],"concerning":[255],"value":[258],"No.":[260],"Specifically,":[261],"case":[263],"\u03bb.":[279]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}