{"id":"https://openalex.org/W2902886577","doi":"https://doi.org/10.1002/malq.201800017","title":"Topological elementary equivalence of regular semi\u2010algebraic sets in three\u2010dimensional space","display_name":"Topological elementary equivalence of regular semi\u2010algebraic sets in three\u2010dimensional space","publication_year":2018,"publication_date":"2018-12-01","ids":{"openalex":"https://openalex.org/W2902886577","doi":"https://doi.org/10.1002/malq.201800017","mag":"2902886577"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201800017","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201800017","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","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":["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/A5087587379","display_name":"Floris Geerts","orcid":"https://orcid.org/0000-0002-8967-2473"},"institutions":[{"id":"https://openalex.org/I149213910","display_name":"University of Antwerp","ror":"https://ror.org/008x57b05","country_code":"BE","type":"education","lineage":["https://openalex.org/I149213910"]},{"id":"https://openalex.org/I4210111370","display_name":"ZNA Middelheim Hospital","ror":"https://ror.org/01z5jvj74","country_code":"BE","type":"healthcare","lineage":["https://openalex.org/I4210111370"]},{"id":"https://openalex.org/I4210119540","display_name":"Province of Antwerp","ror":"https://ror.org/022v8s261","country_code":"BE","type":"government","lineage":["https://openalex.org/I4210119540"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Floris Geerts","raw_affiliation_strings":["Department of Mathematics and Computer Science Universiteit Antwerpen Middelheimlaan 1 Antwerpen 2020 Belgium","Department of Mathematics and Computer Science, Universiteit Antwerpen, Middelheimlaan 1, Antwerpen, 2020 Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science Universiteit Antwerpen Middelheimlaan 1 Antwerpen 2020 Belgium","institution_ids":["https://openalex.org/I149213910","https://openalex.org/I4210111370","https://openalex.org/I4210119540"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Universiteit Antwerpen, Middelheimlaan 1, Antwerpen, 2020 Belgium","institution_ids":["https://openalex.org/I149213910"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035702185","display_name":"Bart Kuijpers","orcid":"https://orcid.org/0000-0001-5774-0948"},"institutions":[{"id":"https://openalex.org/I878454856","display_name":"Hasselt University","ror":"https://ror.org/04nbhqj75","country_code":"BE","type":"education","lineage":["https://openalex.org/I878454856"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Bart Kuijpers","raw_affiliation_strings":["Databases and Theoretical Computer Science Research Group Universiteit Hasselt &amp; Transnationale Universiteit Limburg Agoralaan, Gebouw D Diepenbeek 3590 Belgium","Databases and Theoretical Computer Science Research Group, Universiteit Hasselt & Transnationale Universiteit Limburg, Agoralaan, Gebouw D, Diepenbeek, 3590 Belgium"],"raw_orcid":"https://orcid.org/0000-0001-5774-0948","affiliations":[{"raw_affiliation_string":"Databases and Theoretical Computer Science Research Group Universiteit Hasselt &amp; Transnationale Universiteit Limburg Agoralaan, Gebouw D Diepenbeek 3590 Belgium","institution_ids":["https://openalex.org/I878454856"]},{"raw_affiliation_string":"Databases and Theoretical Computer Science Research Group, Universiteit Hasselt & Transnationale Universiteit Limburg, Agoralaan, Gebouw D, Diepenbeek, 3590 Belgium","institution_ids":["https://openalex.org/I878454856"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5035702185"],"corresponding_institution_ids":["https://openalex.org/I878454856"],"apc_list":{"value":2900,"currency":"USD","value_usd":2900},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18072778,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"6","first_page":"435","last_page":"463"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9983000159263611,"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/T11567","display_name":"semigroups and automata theory","score":0.9983000159263611,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9916999936103821,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9905999898910522,"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":0.8540121912956238},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.5862399339675903},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5355845093727112},{"id":"https://openalex.org/keywords/connected-space","display_name":"Connected space","score":0.5001440048217773},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.488369882106781},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.46487167477607727},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.408809095621109},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4060624837875366},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34981703758239746},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3252132534980774},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22033753991127014},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09932953119277954}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8540121912956238},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.5862399339675903},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5355845093727112},{"id":"https://openalex.org/C24977911","wikidata":"https://www.wikidata.org/wiki/Q1491995","display_name":"Connected space","level":3,"score":0.5001440048217773},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.488369882106781},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.46487167477607727},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.408809095621109},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4060624837875366},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34981703758239746},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3252132534980774},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22033753991127014},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09932953119277954},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1002/malq.201800017","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201800017","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","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:c:irua:156047","is_oa":false,"landing_page_url":"https://hdl.handle.net/10067/1560470151162165141","pdf_url":null,"source":{"id":"https://openalex.org/S4377196495","display_name":"Anet (University of Antwerp)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149213910","host_organization_name":"University of Antwerp","host_organization_lineage":["https://openalex.org/I149213910"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:documentserver.uhasselt.be:1942/23448","is_oa":false,"landing_page_url":"http://hdl.handle.net/1942/23448","pdf_url":null,"source":{"id":"https://openalex.org/S4306401926","display_name":"Document Server@UHasselt (UHasselt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I878454856","host_organization_name":"Hasselt University","host_organization_lineage":["https://openalex.org/I878454856"],"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":"info:eu-repo/semantics/report"},{"id":"pmh:oai:documentserver.uhasselt.be:1942/25875","is_oa":false,"landing_page_url":"http://hdl.handle.net/1942/25875","pdf_url":null,"source":{"id":"https://openalex.org/S4306401926","display_name":"Document Server@UHasselt (UHasselt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I878454856","host_organization_name":"Hasselt University","host_organization_lineage":["https://openalex.org/I878454856"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W59373101","https://openalex.org/W124550681","https://openalex.org/W377720107","https://openalex.org/W1444781587","https://openalex.org/W1510170913","https://openalex.org/W1879819495","https://openalex.org/W1966915419","https://openalex.org/W1989267168","https://openalex.org/W2002211861","https://openalex.org/W2037381552","https://openalex.org/W2072686809","https://openalex.org/W2084875013","https://openalex.org/W2094548115","https://openalex.org/W2105059047","https://openalex.org/W2138402044","https://openalex.org/W2153167702","https://openalex.org/W2162052349","https://openalex.org/W2176172793","https://openalex.org/W2285989144","https://openalex.org/W2610592248","https://openalex.org/W3139934447","https://openalex.org/W4212859549","https://openalex.org/W4240514825","https://openalex.org/W4246140018","https://openalex.org/W4249738637","https://openalex.org/W4251216716","https://openalex.org/W4298290503","https://openalex.org/W4299498003","https://openalex.org/W4299599836","https://openalex.org/W4299992305","https://openalex.org/W4300596011"],"related_works":["https://openalex.org/W2088544526","https://openalex.org/W2964187826","https://openalex.org/W1748582773","https://openalex.org/W3091611190","https://openalex.org/W2316140067","https://openalex.org/W2375255986","https://openalex.org/W3022714090","https://openalex.org/W2354885222","https://openalex.org/W2089625688","https://openalex.org/W2380895929"],"abstract_inverted_index":{"Abstract":[0],"We":[1,21],"consider":[2],"semi\u2010algebraic":[3,38,58,84,107],"sets":[4,9,39,59,85,108,117],"and":[5,62,109],"properties":[6,26],"of":[7,33,77,81,106,126,130],"these":[8],"that":[10,27,113],"are":[11,22,28,40],"expressible":[12],"by":[13,50,124],"sentences":[14],"in":[15,24,60,68,86],"first\u2010order":[16,25,53,137],"logic":[17],"over":[18],"the":[19,34,94,102,110],"reals.":[20],"interested":[23],"invariant":[29],"under":[30],"topological":[31,52,78,104],"transformations":[32],"ambient":[35],"space.":[36],"Two":[37],"called":[41],"topologically":[42,114],"elementarily":[43,115],"equivalent":[44,116],"if":[45],"they":[46],"cannot":[47],"be":[48,119],"distinguished":[49],"such":[51],"sentences.":[54],"So":[55],"far,":[56],"only":[57],"one":[61],"two\u2010dimensional":[63,95],"space":[64],"have":[65],"been":[66],"considered":[67],"this":[69],"context.":[70],"Our":[71,97],"contribution":[72],"is":[73,99],"a":[74,90,133,136],"natural":[75],"characterisation":[76,92,98],"elementary":[79],"equivalence":[80],"regular":[82],"closed":[83],"three\u2010dimensional":[87],"space,":[88],"extending":[89],"known":[91],"for":[93],"case.":[96],"based":[100],"on":[101],"local":[103],"behaviour":[105],"key":[111],"observation":[112],"can":[118],"transformed":[120],"into":[121],"each":[122,129],"other":[123],"means":[125],"geometric":[127],"transformations,":[128],"them":[131],"mapping":[132],"set":[134],"to":[135],"indistinguishable":[138],"one.":[139]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
