{"id":"https://openalex.org/W2025879964","doi":"https://doi.org/10.2307/2586690","title":"Quasi-o-minimal structures","display_name":"Quasi-o-minimal structures","publication_year":2000,"publication_date":"2000-09-01","ids":{"openalex":"https://openalex.org/W2025879964","doi":"https://doi.org/10.2307/2586690","mag":"2025879964"},"language":"en","primary_location":{"id":"doi:10.2307/2586690","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586690","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/A5038551042","display_name":"Oleg Belegradek","orcid":null},"institutions":[{"id":"https://openalex.org/I118036225","display_name":"Istanbul Bilgi University","ror":"https://ror.org/04pm4x478","country_code":"TR","type":"education","lineage":["https://openalex.org/I118036225"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Oleg Belegradek","raw_affiliation_strings":["Department of Mathematics and Computer Science, Istanbul Bilgi University, In\u00f6n\u00fc Caddesi No.28, Ku\u015ftepe 80310. \u015ei\u015fli, Istanbul, Turkey E-mail:","Department of Mathematics and Computer Science, Istanbul Bilgi University, In\u00f6n\u00fc Caddesi No.28, Ku\u015ftepe 80310. \u015ei\u015fli, Istanbul, Turkey E-mail: olegb@bilgi.edu.tr"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Istanbul Bilgi University, In\u00f6n\u00fc Caddesi No.28, Ku\u015ftepe 80310. \u015ei\u015fli, Istanbul, Turkey E-mail:","institution_ids":["https://openalex.org/I118036225"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Istanbul Bilgi University, In\u00f6n\u00fc Caddesi No.28, Ku\u015ftepe 80310. \u015ei\u015fli, Istanbul, Turkey E-mail: olegb@bilgi.edu.tr","institution_ids":["https://openalex.org/I118036225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047276331","display_name":"Ya\u2019acov Peterzil","orcid":null},"institutions":[{"id":"https://openalex.org/I91203450","display_name":"University of Haifa","ror":"https://ror.org/02f009v59","country_code":"IL","type":"education","lineage":["https://openalex.org/I91203450"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ya'acov Peterzil","raw_affiliation_strings":["Department of Mathematics, University of Haifa, Haifa, Israel E-mail:","Department of Mathematics, University of Haifa, Haifa, Israel E-mail: kobi@mathcs2.haifa.ac.il"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Haifa, Haifa, Israel E-mail:","institution_ids":["https://openalex.org/I91203450"]},{"raw_affiliation_string":"Department of Mathematics, University of Haifa, Haifa, Israel E-mail: kobi@mathcs2.haifa.ac.il","institution_ids":["https://openalex.org/I91203450"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113593194","display_name":"Frank Olaf Wagner","orcid":null},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Frank Wagner","raw_affiliation_strings":["Institut Girard Desargues, Universite Claude Bernard, Mathematiques, Batiment 101, 43, Boulevard du 11 November 1918, 69622 Villeurbanne-Cedex, France E-mail:","Institut Girard Desargues, Universite Claude Bernard, Mathematiques, Batiment 101, 43, Boulevard du 11 November 1918, 69622 Villeurbanne-Cedex, France E-mail: wagner@desargues.univ-lyonl.fr"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Girard Desargues, Universite Claude Bernard, Mathematiques, Batiment 101, 43, Boulevard du 11 November 1918, 69622 Villeurbanne-Cedex, France E-mail:","institution_ids":["https://openalex.org/I100532134"]},{"raw_affiliation_string":"Institut Girard Desargues, Universite Claude Bernard, Mathematiques, Batiment 101, 43, Boulevard du 11 November 1918, 69622 Villeurbanne-Cedex, France E-mail: wagner@desargues.univ-lyonl.fr","institution_ids":["https://openalex.org/I100532134"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038551042"],"corresponding_institution_ids":["https://openalex.org/I118036225"],"apc_list":null,"apc_paid":null,"fwci":2.5094,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.88187039,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"65","issue":"3","first_page":"1115","last_page":"1132"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9872000217437744,"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":0.9872000217437744,"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":0.9789000153541565,"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":0.9146999716758728,"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/mathematics","display_name":"Mathematics","score":0.8253166675567627},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.6393691301345825},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6231945753097534},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5968987941741943},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5165671110153198},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.4625052809715271},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4275960624217987},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42590880393981934},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.41066282987594604}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8253166675567627},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.6393691301345825},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6231945753097534},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5968987941741943},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5165671110153198},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.4625052809715271},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4275960624217987},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42590880393981934},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.41066282987594604},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2586690","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586690","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/1183746171","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183746171","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":12,"referenced_works":["https://openalex.org/W76696758","https://openalex.org/W584440261","https://openalex.org/W631147175","https://openalex.org/W1593439579","https://openalex.org/W2005659848","https://openalex.org/W2010757891","https://openalex.org/W2031773420","https://openalex.org/W2070703446","https://openalex.org/W2092583023","https://openalex.org/W2574666458","https://openalex.org/W2971268466","https://openalex.org/W4233980873"],"related_works":["https://openalex.org/W2152992791","https://openalex.org/W2378598099","https://openalex.org/W2611275940","https://openalex.org/W2367539883","https://openalex.org/W1919101720","https://openalex.org/W2370553949","https://openalex.org/W4297833975","https://openalex.org/W2934154379","https://openalex.org/W2052067742","https://openalex.org/W2953384352"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"structure":[2,14],"(":[3],"M":[4],",":[5],"&lt;,":[6],"\u2026)":[7],"is":[8,49,80,86,100,108,120],"called":[9],"quasi-o-minimal":[10,40,67,77,83,96,103],"if":[11],"in":[12,117],"any":[13,76,82],"elementarily":[15],"equivalent":[16],"to":[17,59,65],"it":[18,64],"the":[19,24,50,121],"definable":[20],"subsets":[21,29],"are":[22,43],"exactly":[23],"Boolean":[25],"combinations":[26],"of":[27,36,39,47,53,115,123,125],"0-definable":[28],"and":[30,62],"intervals.":[31],"We":[32,55,110],"give":[33],"a":[34,57,87,113],"series":[35],"natural":[37],"examples":[38],"structures":[41],"which":[42],"not":[44],"o-minimal;":[45,101],"one":[46],"them":[48],"ordered":[51,68,78,84,98,106],"group":[52,79,99,107],"integers.":[54],"develop":[56],"technique":[58],"investigate":[60],"quasi-o-minimality":[61,116],"use":[63],"study":[66],"groups":[69],"(possibly":[70],"with":[71],"extra":[72],"structure).":[73],"Main":[74],"results:":[75],"abelian;":[81],"ring":[85],"real":[88],"closed":[89],"field,":[90],"or":[91],"has":[92],"zero":[93],"multiplication;":[94],"every":[95,102],"divisible":[97],"archimedian":[104],"densely":[105],"divisible.":[109],"show":[111],"that":[112],"counterpart":[114],"stability":[118],"theory":[119,124],"notion":[122],"U":[126],"-rank":[127],"1.":[128]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
