{"id":"https://openalex.org/W2138493912","doi":"https://doi.org/10.2307/2273987","title":"A note on nonmultidimensional superstable theories","display_name":"A note on nonmultidimensional superstable theories","publication_year":1985,"publication_date":"1985-12-01","ids":{"openalex":"https://openalex.org/W2138493912","doi":"https://doi.org/10.2307/2273987","mag":"2138493912"},"language":"en","primary_location":{"id":"doi:10.2307/2273987","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273987","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/A5110147319","display_name":"Anand Pillay","orcid":"https://orcid.org/0000-0002-2471-4097"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Anand Pillay","raw_affiliation_strings":["Department of Mathematics, McGill University, Montreal, Canada","Department of Mathematics, McGill University Montreal, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, McGill University, Montreal, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"Department of Mathematics, McGill University Montreal, Canada","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056929763","display_name":"Charles Steinhorn","orcid":null},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Charles Steinhorn","raw_affiliation_strings":["Department of Mathematics, McGill University, Montreal, Canada","Department of Mathematics, McGill University Montreal, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, McGill University, Montreal, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"Department of Mathematics, McGill University Montreal, Canada","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056929763"],"corresponding_institution_ids":["https://openalex.org/I5023651"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.2853598,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"50","issue":"4","first_page":"1020","last_page":"1024"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9623000025749207,"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":0.9623000025749207,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7788395881652832},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.7208772897720337},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.5290229320526123},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5223344564437866},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4778446853160858},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4195594787597656}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7788395881652832},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.7208772897720337},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.5290229320526123},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5223344564437866},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4778446853160858},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4195594787597656},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273987","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273987","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/1183741974","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183741974","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":6,"referenced_works":["https://openalex.org/W2005659848","https://openalex.org/W2014553533","https://openalex.org/W2061701929","https://openalex.org/W2070703446","https://openalex.org/W2384370064","https://openalex.org/W4233980873"],"related_works":["https://openalex.org/W1631776469","https://openalex.org/W4230581126","https://openalex.org/W2950866767","https://openalex.org/W4299610791","https://openalex.org/W2052371115","https://openalex.org/W2911814645","https://openalex.org/W3022703518","https://openalex.org/W2541640833","https://openalex.org/W4206367340","https://openalex.org/W2086359902"],"abstract_inverted_index":{"In":[0,38],"this":[1,43],"paper":[2],"we":[3,48,268],"prove":[4],"that":[5,112,204,279,317,326],"if":[6],"T":[7,30,109,126,145,153,308,315],"is":[8,18,34,127,297,324],"the":[9,23,39,70,113,128,131,303],"complete":[10],"elementary":[11],"diagram":[12],"of":[13,41,72,99,115,130,133,201,302,307,314],"a":[14,19,50,54,96,100,116,120,185,199],"countable":[15],"structure":[16],"and":[17,79,162,182,220,323],"theory":[20,56],"as":[21,75],"in":[22,45,77,106],"title,":[24],"then":[25,169],"Vaught's":[26],"conjecture":[27],"holds":[28],"for":[29,53,184,214,232,255,271],".":[31,140,154,177,236,260,278,334],"This":[32],"result":[33],"Theorem":[35,46],"7,":[36],"below.":[37],"process":[40],"establishing":[42],"proposition,":[44],"3":[47],"give":[49],"sufficient":[51],"condition":[52],"superstable":[55],"having":[57],"only":[58],"countably":[59],"many":[60],"types":[61,135,320],"without":[62],"parameters":[63],"to":[64,103],"be":[65,82,146,198],"\u03c9":[66],"-stable.":[67],"Familiarity":[68],"with":[69],"rudiments":[71],"stability":[73],"theory,":[74],"presented":[76],"[3]":[78],"[4],":[80],"will":[81],"supposed":[83],"throughout.":[84],"The":[85],"notation":[86],"used":[87],"is,":[88],"by":[89,94],"now,":[90],"standard.":[91],"We":[92,179],"begin":[93],"giving":[95],"new":[97],"proof":[98],"lemma":[101],"due":[102],"J.":[104],"Saffe":[105],"[6].":[107],"For":[108,291],"stable,":[110],"recall":[111],"multiplicity":[114,161,176],"type":[117],"p":[118,139],"over":[119,136,321],"set":[121],"A":[122,137,149,157,164,171,208,212,224,230,247,253,263,283,289,322],"\u2286":[123,150],"\u2133":[124,151],"\u22a8":[125,152],"cardinality":[129],"collection":[132],"strong":[134,319],"extending":[138],"Lemma":[141],"1":[142],"(Saffe).":[143],"Let":[144,187],"stable":[147],",":[148,207,219,223,229,246,274,282,288],"If":[155],"t(b\u0304,":[156,170,211],")":[158,165,209,213,225,231,248,254,264,284,316,330],"has":[159,166,174,265],"infinite":[160,175],"t(c\u0304,":[163,262],"finite":[167,266],"multiplicity,":[168,267],"\u222a":[172],"{c\u0304})":[173],"Proof.":[178],"suppose":[180],"not":[181],"work":[183],"contradiction.":[186],"\u2039b\u0304":[188],"\u03b3":[189,191,206,216,222,233,240,243,245,257,273,281,293,301,329],":":[190],"\u2264":[192,217],"\u03b1":[193,195,218,259,277,295],"\u203a,":[194],"\u2265":[196],"\u03c9,":[197],"list":[200],"elements":[202],"so":[203],"t(b\u0304":[205,242,250],"=":[210,249,285,331],"all":[215,272],"st(b\u0304":[221,227],"\u2260":[226,234],"\u03b4":[228,235,275,287],"Furthermore,":[237],"let":[238],"c\u0304":[239,332],"satisfy":[241],"\u2227c\u0304":[244],"\u2227":[251],"c\u0304,":[252],"each":[256,292],"<":[258,276,294],"Since":[261],"may":[269],"assume":[270],"st(c\u0304":[280,286],").":[290],"there":[296],"an":[298],"automorphism":[299],"f":[300,327],"so-called":[304],"\u201cmonster":[305],"model\u201d":[306],"(a":[309],"sufficiently":[310],"large,":[311],"saturated":[312],"model":[313],"preserves":[318],"such":[325],"(c\u0304":[328],"0":[333]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}