{"id":"https://openalex.org/W2009183820","doi":"https://doi.org/10.2307/2275610","title":"Existentially closed models via constructible sets: There are 2\u21350 existentially closed pairwise non elementarily equivalent existentially closed ordered groups","display_name":"Existentially closed models via constructible sets: There are 2\u21350 existentially closed pairwise non elementarily equivalent existentially closed ordered groups","publication_year":1996,"publication_date":"1996-03-01","ids":{"openalex":"https://openalex.org/W2009183820","doi":"https://doi.org/10.2307/2275610","mag":"2009183820"},"language":"en","primary_location":{"id":"doi:10.2307/2275610","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275610","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/A5003220876","display_name":"Anatole Kh\u00e9lif","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"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Anatole Khelif","raw_affiliation_strings":["UFR de Math\u00e9matiques, Equipe de Logique, Universit\u00e9 Paris VII, 2, Place Jussieu, 75251 Paris Cedex 05, France, E-mail:","UNIVERSITE PARIS VII"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UFR de Math\u00e9matiques, Equipe de Logique, Universit\u00e9 Paris VII, 2, Place Jussieu, 75251 Paris Cedex 05, France, E-mail:","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I3017942884"]},{"raw_affiliation_string":"UNIVERSITE PARIS VII","institution_ids":["https://openalex.org/I204730241"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003220876"],"corresponding_institution_ids":["https://openalex.org/I204730241","https://openalex.org/I3017942884"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.13863364,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"61","issue":"1","first_page":"277","last_page":"284"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9907000064849854,"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"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9907000064849854,"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"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9776999950408936,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9666000008583069,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.7865355610847473},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.7772371172904968},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5022587776184082},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4824998378753662},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.46019721031188965},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.42077693343162537},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3596852123737335},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.18030884861946106},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.05104556679725647}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7865355610847473},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.7772371172904968},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5022587776184082},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4824998378753662},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.46019721031188965},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.42077693343162537},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3596852123737335},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.18030884861946106},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05104556679725647},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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":1,"locations":[{"id":"doi:10.2307/2275610","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275610","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W13432289","https://openalex.org/W1484200610","https://openalex.org/W1495067201","https://openalex.org/W1969046746","https://openalex.org/W1998286202","https://openalex.org/W2013544047","https://openalex.org/W2117060314","https://openalex.org/W2316896557","https://openalex.org/W2330548796"],"related_works":["https://openalex.org/W2487162673","https://openalex.org/W2793211469","https://openalex.org/W2949152769","https://openalex.org/W4372354731","https://openalex.org/W2562400057","https://openalex.org/W1692008701","https://openalex.org/W2597588799","https://openalex.org/W4360593462","https://openalex.org/W2090927286","https://openalex.org/W2986762086"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"prove":[2],"that":[3,37],"there":[4],"are":[5],"2\u03c70":[6],"pairwise":[7],"non":[8],"elementarily":[9],"equivalent":[10],"existentially":[11],"closed":[12],"ordered":[13,41,51],"groups,":[14],"which":[15,81],"solve":[16],"the":[17,34,38,47,50,78],"main":[18,62],"open":[19],"problem":[20],"in":[21,71],"this":[22],"area":[23],"(cf.":[24,84],"[3,":[25],"10]).":[26],"A":[27],"simple":[28],"direct":[29],"proof":[30],"is":[31,58,86],"given":[32],"of":[33,40,49],"weaker":[35],"fact":[36],"theory":[39],"groups":[42],"has":[43],"no":[44],"model":[45],"companion;":[46],"case":[48],"division":[52],"rings":[53],"over":[54],"a":[55],"field":[56],"k":[57],"also":[59],"investigated.":[60],"Our":[61],"result":[63],"uses":[64],"constructible":[65],"sets":[66],"and":[67],"can":[68],"be":[69],"put":[70],"an":[72],"abstract":[73],"general":[74],"framework.":[75],"Comparison":[76],"with":[77],"standard":[79],"methods":[80],"use":[82],"forcing":[83],"[4])":[85],"sketched.":[87]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}