{"id":"https://openalex.org/W2075687506","doi":"https://doi.org/10.2307/2275706","title":"On the number of models of uncountable theories","display_name":"On the number of models of uncountable theories","publication_year":1994,"publication_date":"1994-12-01","ids":{"openalex":"https://openalex.org/W2075687506","doi":"https://doi.org/10.2307/2275706","mag":"2075687506"},"language":"en","primary_location":{"id":"doi:10.2307/2275706","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275706","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/A5083957740","display_name":"Ambar Chowdhury","orcid":null},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Ambar Chowdhury","raw_affiliation_strings":["Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada, L8S 4K1, E-mail:","McMaster university#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada, L8S 4K1, E-mail:","institution_ids":["https://openalex.org/I98251732"]},{"raw_affiliation_string":"McMaster university#TAB#","institution_ids":["https://openalex.org/I98251732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110147319","display_name":"Anand Pillay","orcid":"https://orcid.org/0000-0002-2471-4097"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anand Pillay","raw_affiliation_strings":["Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, E-mail:","University of Notre Dame"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, E-mail:","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"University of Notre Dame","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5083957740"],"corresponding_institution_ids":["https://openalex.org/I98251732"],"apc_list":null,"apc_paid":null,"fwci":0.99,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.74211141,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"4","first_page":"1285","last_page":"1300"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9848999977111816,"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":0.9848999977111816,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9447000026702881,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uncountable-set","display_name":"Uncountable set","score":0.96378493309021},{"id":"https://openalex.org/keywords/transcendental-number","display_name":"Transcendental number","score":0.8103697896003723},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7551167607307434},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6991868019104004},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5115812420845032},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5113863348960876},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4077262282371521},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.09899139404296875},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07787060737609863}],"concepts":[{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.96378493309021},{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.8103697896003723},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7551167607307434},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6991868019104004},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5115812420845032},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5113863348960876},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4077262282371521},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.09899139404296875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07787060737609863},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2275706","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275706","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/1183744626","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183744626","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W134345042","https://openalex.org/W1480542034","https://openalex.org/W1631776469","https://openalex.org/W1991789901","https://openalex.org/W1993603861","https://openalex.org/W2015279225","https://openalex.org/W2055344668","https://openalex.org/W2061701929","https://openalex.org/W2068300269","https://openalex.org/W2084009057","https://openalex.org/W2086697475","https://openalex.org/W2108179031","https://openalex.org/W4241755248","https://openalex.org/W4298194724"],"related_works":["https://openalex.org/W2100222222","https://openalex.org/W1982069151","https://openalex.org/W2256572025","https://openalex.org/W4303646992","https://openalex.org/W2952146172","https://openalex.org/W4379919445","https://openalex.org/W2766907287","https://openalex.org/W196788981","https://openalex.org/W24519920","https://openalex.org/W2185713319"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"we":[4],"establish":[5],"the":[6],"following":[7],"theorems.":[8],"Theorem":[9,54],"A.":[10],"Let":[11,56,65],"T":[12,26,28,35,45,48,57],"be":[13,58,69,86],"a":[14,70],"complete":[15],"first-order":[16],"theory":[17],"which":[18,77,92],"is":[19,36,101],"uncountable,":[20],"Then":[21,99],":":[22],"(i)":[23],"I":[24],"(\u2223":[25],"\u2223,":[27,46],")":[29,49,68],"\u2265":[30,43,50],"\u2135":[31,51],"0":[32,52],"(ii)":[33],"If":[34],"not":[37,60,79],"unidimensional,":[38],"then":[39],"for":[40],"any":[41,87],"\u03bb":[42],"\u2223":[44],"I(\u03bb,":[47],".":[53,106],"B.":[55],"superstable,":[59],"totally":[61],"transcendental":[62],"and":[63,83,103],"nonmultidimensional.":[64],"\u03b8(":[66],"x":[67],"formula":[71],"of":[72,90],"least":[73],"R":[74],"\u221e":[75],"rank":[76],"does":[78],"have":[80,96],"Morley":[81,97],"rank,":[82],"let":[84],"p":[85,100],"stationary":[88],"completion":[89],"\u03b8":[91],"also":[93],"fails":[94],"to":[95],"rank.":[98],"regular":[102],"locally":[104],"modular":[105]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
