{"id":"https://openalex.org/W2065640874","doi":"https://doi.org/10.2307/2272166","title":"Semi-minimal theories and categoricity","display_name":"Semi-minimal theories and categoricity","publication_year":1975,"publication_date":"1975-09-01","ids":{"openalex":"https://openalex.org/W2065640874","doi":"https://doi.org/10.2307/2272166","mag":"2065640874"},"language":"en","primary_location":{"id":"doi:10.2307/2272166","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2272166","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/A5028084715","display_name":"Daniel Andler","orcid":null},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Daniel Andler","raw_affiliation_strings":["Universit\u00e9 Paris VII, 75005 Paris, France","UNIVERSITE PARIS VII"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris VII, 75005 Paris, France","institution_ids":["https://openalex.org/I204730241"]},{"raw_affiliation_string":"UNIVERSITE PARIS VII","institution_ids":["https://openalex.org/I204730241"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028084715"],"corresponding_institution_ids":["https://openalex.org/I204730241"],"apc_list":null,"apc_paid":null,"fwci":0.5807,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.69154412,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"40","issue":"3","first_page":"419","last_page":"438"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998000264167786,"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":0.9998000264167786,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.9955000281333923,"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/uncountable-set","display_name":"Uncountable set","score":0.9702222943305969},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8458254337310791},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.8094334006309509},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7754489183425903},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.6071685552597046},{"id":"https://openalex.org/keywords/model-theory","display_name":"Model theory","score":0.5725563764572144},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5238685011863708},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.4961114823818207},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3969070315361023},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3712642192840576},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36986681818962097},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.09698486328125},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.0692792534828186}],"concepts":[{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.9702222943305969},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8458254337310791},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.8094334006309509},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7754489183425903},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.6071685552597046},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.5725563764572144},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5238685011863708},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.4961114823818207},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3969070315361023},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3712642192840576},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36986681818962097},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.09698486328125},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0692792534828186},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2272166","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2272166","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/1183739474","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183739474","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":19,"referenced_works":["https://openalex.org/W918671874","https://openalex.org/W1593399533","https://openalex.org/W1951287835","https://openalex.org/W1989141787","https://openalex.org/W2002241640","https://openalex.org/W2028791022","https://openalex.org/W2060284566","https://openalex.org/W2065143293","https://openalex.org/W2066091881","https://openalex.org/W2069204363","https://openalex.org/W2093973703","https://openalex.org/W2134675812","https://openalex.org/W2215148284","https://openalex.org/W2601523163","https://openalex.org/W2799061192","https://openalex.org/W2977904728","https://openalex.org/W4235178139","https://openalex.org/W4247248535","https://openalex.org/W6735779031"],"related_works":["https://openalex.org/W3019662020","https://openalex.org/W4297571715","https://openalex.org/W2100222222","https://openalex.org/W2512721618","https://openalex.org/W2600675026","https://openalex.org/W3139954723","https://openalex.org/W4242301765","https://openalex.org/W1519257018","https://openalex.org/W2488350907","https://openalex.org/W3097468110"],"abstract_inverted_index":{"The":[0,123],"study":[1,209],"of":[2,42,69,80,102,158,169,226,249,254,267],"countable":[3,27,54,70],"theories":[4,211],"categorical":[5,29,35,56,132,142,173],"in":[6,18,30,36,57,133,143,161,174,181,213,260,264],"some":[7,31,58,134,214,239,278],"uncountable":[8,32,38,59,121],"power":[9,33,60,135,162],"was":[10,74,148],"initiated":[11],"by":[12,76,83,150],"\u0141o\u015b":[13,125,251],"and":[14,16,46,105,208,253],"Vaught":[15],"developed":[17,82],"two":[19],"stages.":[20],"First,":[21],"Morley":[22,256],"proved":[23],"(1962)":[24],"that":[25,52,128,183],"a":[26,40,53,78,99,129,170,227,268],"theory":[28,55,130,171,229,270],"is":[34,141],"every":[37,144],"power,":[39],"conjecture":[41,51,104,126,197,252,257],"\u0141o\u015b.":[43],"Second,":[44],"Baldwin":[45],"Lachlan":[47],"confirmed":[48],"(1969)":[49],"Vaught's":[50,107],"has":[61],"either":[62],"one":[63],"or":[64],"countably":[65],"many":[66],"isomorphism":[67],"types":[68],"models.":[71],"That":[72],"result":[73],"obtained":[75],"pursuing":[77],"line":[79],"research":[81],"Marsh":[84],"(1966).":[85],"For":[86],"certain":[87],"well-behaved":[88],"theories,":[89],"which":[90,231],"he":[91],"called":[92],"strongly":[93,218],"minimal":[94,219],",":[95,179],"Marsh's":[96,217],"method":[97,245],"yielded":[98],"simple":[100,247],"proof":[101],"\u0141o\u015b's":[103],"settled":[106,149],"conjecture.":[108],"In":[109],"recent":[110],"years":[111],"efforts":[112],"have":[113],"been":[114],"made":[115],"to":[116,120,194,216],"extend":[117],"these":[118],"results":[119,274],"theories.":[122,221],"generalized":[124],"states":[127],"T":[131,139,164,172,176,230,262,271],"greater":[136],"than":[137],"\u2223":[138,140,163,165,175,177,261],"such":[145,191],"power.":[146],"It":[147],"Shelah":[151,153],"(1970).":[152],"then":[154],"raised":[155],"the":[156,159,199,203,224,250,255,265],"question":[157],"models":[160,225],"=":[166],"\u2135":[167,189],"\u03b1":[168],"+":[178,188],"conjecturing":[180],"[S3]":[182],"there":[184],"are":[185,280],"exactly":[186],"\u2223\u03b1\u2223":[187],"0":[190],"models,":[192],"up":[193],"isomorphism.":[195],"This":[196],"provided":[198],"initial":[200],"motivation":[201],"for":[202],"present":[204],"work.":[205],"We":[206,222],"define":[207],"semi-minimal":[210,228,269],"analogous":[212],"ways":[215],"(countable)":[220],"describe":[223],"contain":[232],"an":[233],"infinite":[234],"indiscernible":[235],"set.":[236],"Besides":[237],"throwing":[238],"light":[240],"on":[241,258],"Shelah's":[242],"conjecture,":[243],"our":[244],"gives":[246],"proofs":[248],"categoricity":[259],"\u2223,":[263],"case":[266],".":[272],"Other":[273],"as":[275,277],"well":[276],"examples":[279],"provided.":[281]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}