{"id":"https://openalex.org/W3210636447","doi":"https://doi.org/10.1002/malq.202200004","title":"Tameness of definably complete locally o\u2010minimal structures and definable bounded multiplication","display_name":"Tameness of definably complete locally o\u2010minimal structures and definable bounded multiplication","publication_year":2022,"publication_date":"2022-08-20","ids":{"openalex":"https://openalex.org/W3210636447","doi":"https://doi.org/10.1002/malq.202200004","mag":"3210636447"},"language":"en","primary_location":{"id":"doi:10.1002/malq.202200004","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.202200004","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2110.15613","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064823367","display_name":"Masato Fujita","orcid":"https://orcid.org/0000-0003-1289-5182"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]},{"id":"https://openalex.org/I57772034","display_name":"Japan Coast Guard Academy","ror":"https://ror.org/03qa1nk44","country_code":"JP","type":"education","lineage":["https://openalex.org/I1308952385","https://openalex.org/I4387155174","https://openalex.org/I57772034"]},{"id":"https://openalex.org/I75198481","display_name":"Wakayama University","ror":"https://ror.org/05wr49d48","country_code":"JP","type":"education","lineage":["https://openalex.org/I75198481"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masato Fujita","raw_affiliation_strings":["Department of Liberal Arts Japan Coast Guard Academy 5\u20101 Wakaba\u2010cho, Kure Hiroshima 737\u20108512 Japan","Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan","Department of Mathematics, Wakayama University, Wakayama, 640-8510, Japan","Department of Liberal Arts, Japan Coast Guard Academy, 5-1 Wakaba-cho, Kure, Hiroshima 737-8512, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Liberal Arts Japan Coast Guard Academy 5\u20101 Wakaba\u2010cho, Kure Hiroshima 737\u20108512 Japan","institution_ids":["https://openalex.org/I57772034"]},{"raw_affiliation_string":"Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan","institution_ids":["https://openalex.org/I146399215"]},{"raw_affiliation_string":"Department of Mathematics, Wakayama University, Wakayama, 640-8510, Japan","institution_ids":["https://openalex.org/I75198481"]},{"raw_affiliation_string":"Department of Liberal Arts, Japan Coast Guard Academy, 5-1 Wakaba-cho, Kure, Hiroshima 737-8512, Japan","institution_ids":["https://openalex.org/I57772034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102434316","display_name":"Tomohiro Kawakami","orcid":null},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]},{"id":"https://openalex.org/I57772034","display_name":"Japan Coast Guard Academy","ror":"https://ror.org/03qa1nk44","country_code":"JP","type":"education","lineage":["https://openalex.org/I1308952385","https://openalex.org/I4387155174","https://openalex.org/I57772034"]},{"id":"https://openalex.org/I75198481","display_name":"Wakayama University","ror":"https://ror.org/05wr49d48","country_code":"JP","type":"education","lineage":["https://openalex.org/I75198481"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tomohiro Kawakami","raw_affiliation_strings":["Department of Mathematics Wakayama University Wakayama 640\u20108510 Japan","Department of Liberal Arts, Japan Coast Guard Academy, 5-1 Wakaba-cho, Kure, Hiroshima 737-8512, Japan","Department of Mathematics, Wakayama University, Wakayama, 640-8510, Japan","Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Wakayama University Wakayama 640\u20108510 Japan","institution_ids":["https://openalex.org/I75198481"]},{"raw_affiliation_string":"Department of Liberal Arts, Japan Coast Guard Academy, 5-1 Wakaba-cho, Kure, Hiroshima 737-8512, Japan","institution_ids":["https://openalex.org/I57772034"]},{"raw_affiliation_string":"Department of Mathematics, Wakayama University, Wakayama, 640-8510, Japan","institution_ids":["https://openalex.org/I75198481"]},{"raw_affiliation_string":"Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008201823","display_name":"Wataru Komine","orcid":null},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]},{"id":"https://openalex.org/I57772034","display_name":"Japan Coast Guard Academy","ror":"https://ror.org/03qa1nk44","country_code":"JP","type":"education","lineage":["https://openalex.org/I1308952385","https://openalex.org/I4387155174","https://openalex.org/I57772034"]},{"id":"https://openalex.org/I75198481","display_name":"Wakayama University","ror":"https://ror.org/05wr49d48","country_code":"JP","type":"education","lineage":["https://openalex.org/I75198481"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Wataru Komine","raw_affiliation_strings":["Institute of Mathematics University of Tsukuba Ibaraki 305\u20108571 Japan","Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan","Department of Mathematics, Wakayama University, Wakayama, 640-8510, Japan","Department of Liberal Arts, Japan Coast Guard Academy, 5-1 Wakaba-cho, Kure, Hiroshima 737-8512, Japan"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics University of Tsukuba Ibaraki 305\u20108571 Japan","institution_ids":["https://openalex.org/I146399215"]},{"raw_affiliation_string":"Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan","institution_ids":["https://openalex.org/I146399215"]},{"raw_affiliation_string":"Department of Mathematics, Wakayama University, Wakayama, 640-8510, Japan","institution_ids":["https://openalex.org/I75198481"]},{"raw_affiliation_string":"Department of Liberal Arts, Japan Coast Guard Academy, 5-1 Wakaba-cho, Kure, Hiroshima 737-8512, Japan","institution_ids":["https://openalex.org/I57772034"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064823367"],"corresponding_institution_ids":["https://openalex.org/I146399215","https://openalex.org/I57772034","https://openalex.org/I75198481"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":2.7976,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.90092704,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"68","issue":"4","first_page":"496","last_page":"515"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998999834060669,"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":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.996399998664856,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9865000247955322,"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":0.8335120677947998},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7616441249847412},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5516607761383057},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5400062799453735},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.507883608341217},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5028955340385437},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4859124720096588},{"id":"https://openalex.org/keywords/locally-compact-space","display_name":"Locally compact space","score":0.4386346638202667},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4324636161327362},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.4216311275959015},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.4113355278968811},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.384758859872818},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2508862614631653},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14582639932632446},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07985487580299377},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07438391447067261}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8335120677947998},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7616441249847412},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5516607761383057},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5400062799453735},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.507883608341217},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5028955340385437},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4859124720096588},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.4386346638202667},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4324636161327362},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4216311275959015},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.4113355278968811},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.384758859872818},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2508862614631653},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14582639932632446},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07985487580299377},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07438391447067261},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/malq.202200004","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.202200004","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2110.15613","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2110.15613","pdf_url":"https://arxiv.org/pdf/2110.15613","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2110.15613","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2110.15613","pdf_url":"https://arxiv.org/pdf/2110.15613","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4399999976158142,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1822440022","https://openalex.org/W1966671634","https://openalex.org/W1972294926","https://openalex.org/W1996195522","https://openalex.org/W2067657455","https://openalex.org/W2081769494","https://openalex.org/W2134929854","https://openalex.org/W2162052349","https://openalex.org/W2550342065","https://openalex.org/W2901322690","https://openalex.org/W2991474283","https://openalex.org/W3004753147","https://openalex.org/W3037987177","https://openalex.org/W3084219209","https://openalex.org/W3092512997","https://openalex.org/W3207065452","https://openalex.org/W4238066263","https://openalex.org/W4281858096","https://openalex.org/W4299599836"],"related_works":["https://openalex.org/W2121543990","https://openalex.org/W2402800040","https://openalex.org/W4252969132","https://openalex.org/W2000020320","https://openalex.org/W2805799113","https://openalex.org/W1981078319","https://openalex.org/W4387315838","https://openalex.org/W2077709279","https://openalex.org/W1449831302","https://openalex.org/W2761453547"],"abstract_inverted_index":{"Abstract":[0],"We":[1,126],"first":[2],"show":[3],"that":[4,102],"the":[5,28,64,99,103,108],"projection":[6],"image":[7],"of":[8,60,66,80,90,105,140],"a":[9,31,35,40,115,119],"discrete":[10,15],"definable":[11,45,124,133],"set":[12],"is":[13,74,118],"again":[14],"for":[16,95,132],"an":[17,69],"arbitrary":[18,70],"definably":[19,55,112,137],"complete":[20,56],"locally":[21,57],"o\u2010minimal":[22,58,78],"structure.":[23],"This":[24],"fact":[25],"together":[26],"with":[27,136],"results":[29],"in":[30],"previous":[32],"paper":[33],"implies":[34],"tame":[36],"dimension":[37],"theory":[38],"and":[39,88,107],"decomposition":[41],"theorem":[42,87,131],"into":[43],"good\u2010shaped":[44],"subsets":[46],"called":[47],"quasi\u2010special":[48],"submanifolds.":[49],"Using":[50],"this":[51],"fact,":[52],"we":[53],"investigate":[54],"expansions":[59,79],"ordered":[61,81],"groups":[62],"when":[63],"restriction":[65],"multiplication":[67],"to":[68,77],"bounded":[71],"open":[72],"box":[73],"definable.":[75],"Similarly":[76],"fields,":[82],"\u0141ojasiewicz's":[83],"inequality,":[84],"Tietze's":[85],"extension":[86],"affiness":[89],"pseudo\u2010definable":[91,109,116],"spaces":[92,110],"hold":[93],"true":[94],"such":[96],"structures":[97],"under":[98],"extra":[100],"assumption":[101],"domains":[104,139],"definition":[106],"are":[111],"compact.":[113],"Here,":[114],"space":[117,121],"topological":[120],"having":[122],"finite":[123],"atlases.":[125],"also":[127],"demonstrate":[128],"Michael's":[129],"selection":[130],"set\u2010valued":[134],"functions":[135],"compact":[138],"definition.":[141]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}
