{"id":"https://openalex.org/W2056631045","doi":"https://doi.org/10.1017/s0022481200051446","title":"Large and small existentially closed structures","display_name":"Large and small existentially closed structures","publication_year":1976,"publication_date":"1976-06-01","ids":{"openalex":"https://openalex.org/W2056631045","doi":"https://doi.org/10.1017/s0022481200051446","mag":"2056631045"},"language":"en","primary_location":{"id":"doi:10.1017/s0022481200051446","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0022481200051446","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/A5049756356","display_name":"Harold Simmons","orcid":null},"institutions":[{"id":"https://openalex.org/I195460627","display_name":"University of Aberdeen","ror":"https://ror.org/016476m91","country_code":"GB","type":"education","lineage":["https://openalex.org/I195460627"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"H. Simmons","raw_affiliation_strings":["University of Aberdeen, King's college, Aberdeen, Scotland AB9 2UB","University of Aberdeen"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Aberdeen, King's college, Aberdeen, Scotland AB9 2UB","institution_ids":["https://openalex.org/I195460627"]},{"raw_affiliation_string":"University of Aberdeen","institution_ids":["https://openalex.org/I195460627"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049756356"],"corresponding_institution_ids":["https://openalex.org/I195460627"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.6377,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.68631897,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"41","issue":"2","first_page":"379","last_page":"390"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9976000189781189,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9959999918937683,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.6544402241706848},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.49300453066825867},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4866991341114044},{"id":"https://openalex.org/keywords/simplicity","display_name":"Simplicity","score":0.4781992435455322},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4553144872188568},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3822105824947357},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36588871479034424},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18217560648918152},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08751589059829712},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0838899314403534}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6544402241706848},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.49300453066825867},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4866991341114044},{"id":"https://openalex.org/C2776372474","wikidata":"https://www.wikidata.org/wiki/Q508291","display_name":"Simplicity","level":2,"score":0.4781992435455322},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4553144872188568},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3822105824947357},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36588871479034424},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18217560648918152},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08751589059829712},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0838899314403534},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0022481200051446","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0022481200051446","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/1183739779","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183739779","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":12,"referenced_works":["https://openalex.org/W572704962","https://openalex.org/W1026413955","https://openalex.org/W1578424393","https://openalex.org/W1987570123","https://openalex.org/W2068828253","https://openalex.org/W2097507397","https://openalex.org/W2132578771","https://openalex.org/W2164658368","https://openalex.org/W2316896557","https://openalex.org/W2410430463","https://openalex.org/W2799061192","https://openalex.org/W6667680397"],"related_works":["https://openalex.org/W2612896625","https://openalex.org/W2596944507","https://openalex.org/W4323715530","https://openalex.org/W2626002520","https://openalex.org/W4367310677","https://openalex.org/W1974360440","https://openalex.org/W2022182753","https://openalex.org/W2157535554","https://openalex.org/W2327343610","https://openalex.org/W1537407126"],"abstract_inverted_index":{"The":[0,155,181],"generic":[1,30,37],"structures":[2,19,31,38,53,63,68,88,119,141,158,231],"introduced":[3],"by":[4,217],"Abraham":[5],"Robinson":[6],"are":[7,32,39,55,110,120,149,159],"now":[8],"well":[9],"established":[10],"in":[11,25,57,95,165,187,206,219],"model":[12,107],"theory.":[13],"Anyone":[14],"who":[15],"works":[16],"with":[17,112,122,193,200],"these":[18],"soon":[20],"begins":[21],"to":[22,48,79,91,130,176],"feel":[23],"that,":[24],"some":[26,146,237],"sense,":[27],"the":[28,35,49,52,58,81,96,103,151,177,201,225,239,242],"infinite":[29],"large":[33,65,82],"and":[34,43,66,83,89,115,125,136,189,196,229,235],"finite":[36],"small.":[40,70],"Here":[41],"\u2018large\u2019":[42],"\u2018small\u2019":[44],"do":[45],"not":[46,160,233],"refer":[47],"cardinality":[50],"of":[51,98,106,134,179,183,203,227,238,241],"but":[54,167],"used":[56],"way":[59],"we":[60,109,128],"describe":[61],"saturated":[62,135],"as":[64,69],"atomic":[67,137],"In":[71,102],"this":[72,171,184],"paper":[73,172,185,208],"I":[74,77,168],"isolate":[75],"what":[76],"consider":[78],"be":[80],"small":[84],"existentially":[85,152],"closed":[86],"(e.c.)":[87],"attempt":[90],"determine":[92],"their":[93],"role":[94],"class":[97],"all":[99,116,123],"e.c.":[100,228,230],"structures.":[101,138,154],"usual":[104],"context":[105],"theory":[108],"concerned":[111,121,199],"elementary":[113],"embeddings":[114,124],"formulas.":[117],"E.c.":[118],"\u22031-formulas.":[126],"Thus":[127],"need":[129],"look":[131],"at":[132],"\u22031-analogues":[133,202],"These":[139],"\u22031-saturated":[140],"have":[142],"been":[143,214],"around":[144],"for":[145],"time;":[147],"they":[148],"just":[150],"universal":[153],"corresponding":[156],"\u22031-atomic":[157,194],"new":[161],"here":[162],"(they":[163],"appear":[164],"[8])":[166],"believe":[169],"that":[170],"will":[173],"add":[174],"much":[175],"understanding":[178],"them.":[180],"bulk":[182],"is":[186,198,232,244],"\u00a7\u00a72":[188],"4.":[190],"\u00a72":[191],"deals":[192],"structures,":[195],"\u00a74":[197],"several":[204],"results":[205],"Vaught's":[207],"[12].":[209],"A":[210],"similar":[211],"program":[212],"has":[213],"carried":[215],"out":[216],"Pouzet":[218],"[6],":[220],"[7],":[221],"[8];":[222],"however,":[223],"there":[224],"significance":[226],"realized":[234],"consequently":[236],"simplicity":[240],"situation":[243],"lost.":[245]},"counts_by_year":[{"year":2021,"cited_by_count":16},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
