{"id":"https://openalex.org/W2017130920","doi":"https://doi.org/10.2307/2273516","title":"Prime and atomic models","display_name":"Prime and atomic models","publication_year":1978,"publication_date":"1978-09-01","ids":{"openalex":"https://openalex.org/W2017130920","doi":"https://doi.org/10.2307/2273516","mag":"2017130920"},"language":"en","primary_location":{"id":"doi:10.2307/2273516","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273516","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/A5112811349","display_name":"Julia F. Knight","orcid":null},"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"]},{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Julia F. Knight","raw_affiliation_strings":["Pennsylvania State University, University Park, PA 16802","University of Notre Dame, Notre Dame, Indiana 46556"],"affiliations":[{"raw_affiliation_string":"Pennsylvania State University, University Park, PA 16802","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"University of Notre Dame, Notre Dame, Indiana 46556","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112811349"],"corresponding_institution_ids":["https://openalex.org/I107639228","https://openalex.org/I130769515"],"apc_list":null,"apc_paid":null,"fwci":0.6807,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.65103556,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"43","issue":"3","first_page":"385","last_page":"393"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9958000183105469,"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/T10849","display_name":"Finite Group Theory Research","score":0.9810000061988831,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.7430172562599182},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.6934643983840942},{"id":"https://openalex.org/keywords/model-theory","display_name":"Model theory","score":0.57936692237854},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5783213973045349},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5667867660522461},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5496646761894226},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5470234155654907},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.503807008266449},{"id":"https://openalex.org/keywords/monomorphism","display_name":"Monomorphism","score":0.4747063219547272},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.4349450170993805},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4080224335193634},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3849026560783386},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33194929361343384},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24009254574775696},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.1322939097881317},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08907461166381836},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.07038718461990356}],"concepts":[{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.7430172562599182},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.6934643983840942},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.57936692237854},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5783213973045349},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5667867660522461},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5496646761894226},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5470234155654907},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.503807008266449},{"id":"https://openalex.org/C100036529","wikidata":"https://www.wikidata.org/wiki/Q1945067","display_name":"Monomorphism","level":3,"score":0.4747063219547272},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.4349450170993805},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4080224335193634},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3849026560783386},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33194929361343384},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24009254574775696},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.1322939097881317},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08907461166381836},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.07038718461990356},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273516","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273516","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/1183740245","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183740245","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":10,"referenced_works":["https://openalex.org/W1593399533","https://openalex.org/W1987131153","https://openalex.org/W2007750284","https://openalex.org/W2036457375","https://openalex.org/W2066091881","https://openalex.org/W2069204363","https://openalex.org/W2075446545","https://openalex.org/W2093337906","https://openalex.org/W2097507397","https://openalex.org/W2134675812"],"related_works":["https://openalex.org/W4283328073","https://openalex.org/W3105928773","https://openalex.org/W2106480630","https://openalex.org/W4299792293","https://openalex.org/W1499331102","https://openalex.org/W177522066","https://openalex.org/W1482930854","https://openalex.org/W2101752691","https://openalex.org/W2402501407","https://openalex.org/W2962677089"],"abstract_inverted_index":{"This":[0,154],"paper":[1],"gives":[2],"some":[3,61],"simple":[4],"existence":[5,41],"results":[6,42,68],"on":[7,141,150],"prime":[8,24,120,133],"and":[9,83,105,109,137,193],"atomic":[10,35,122],"models":[11,59,110,171,187],"over":[12,26,37,124,134],"sets.":[13],"It":[14,166,180],"also":[15,181],"contains":[16,101],"an":[17,34,147],"example":[18],"in":[19,45,58,69,114,158,163,168,177,183,191],"which":[20],"there":[21,32],"is":[22,33,79,85,94,129,156],"no":[23],"model":[25,36,97,123,128,164],"a":[27,80,86,95,115,119,159],"certain":[28,186],"set":[29,52,103],"even":[30],"though":[31],"the":[38,66,76,102],"set.":[39],"The":[40],"are":[43,173,188],"\u201clocal\u201d":[44],"that":[46,100,172,185],"they":[47],"deal":[48],"with":[49,90],"just":[50],"one":[51],"rather":[53],"than":[54],"all":[55,151],"sets":[56,108],"contained":[57],"of":[60,98,118,152,161],"theory.":[62,165],"For":[63],"contrast,":[64],"see":[65],"\u201cglobal\u201d":[67],"[6]":[70],"or":[71,121],"[7,":[72],"p.":[73],"200].":[74],"Throughout":[75],"paper,":[77],"L":[78,88],"countable":[81],"language,":[82],"T":[84,99],"complete":[87],"-theory":[89],"infinite":[91],"models.":[92],"There":[93],"\u201clarge\u201d":[96],"X":[104,125,135,142],"any":[106],"other":[107],"to":[111,131,146],"be":[112,132,144],"used":[113,157],"particular":[116],"construction":[117],".":[126,153],"A":[127],"said":[130],"if":[136],"every":[138],"elementary":[139,148],"monomorphism":[140],"can":[143],"extended":[145],"embedding":[149],"notion":[155],"variety":[160],"ways":[162],"aids":[167,182],"distinguishing":[169],"between":[170],"not":[174],"isomorphic,":[175,189],"as":[176,190],"Vaught":[178],"[10].":[179],"showing":[184],"Baldwin":[192],"Lachlan":[194],"[1].":[195]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}