{"id":"https://openalex.org/W4231630747","doi":"https://doi.org/10.1002/malq.19950410310","title":"Ternary Operations as Primitive Notions for Constructive Plane Geometry VI","display_name":"Ternary Operations as Primitive Notions for Constructive Plane Geometry VI","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W4231630747","doi":"https://doi.org/10.1002/malq.19950410310"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19950410310","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19950410310","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/A5038599115","display_name":"Victor Pambuccian","orcid":"https://orcid.org/0000-0003-2263-1471"},"institutions":[{"id":"https://openalex.org/I4210156717","display_name":"National Research Institute for Veterinary Virology and Microbiology of Russia","ror":"https://ror.org/05ea3hs66","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210156717","https://openalex.org/I4210167168"]},{"id":"https://openalex.org/I47431100","display_name":"Dassault Syst\u00e8mes (France)","ror":"https://ror.org/038sc5x72","country_code":"FR","type":"company","lineage":["https://openalex.org/I47431100"]},{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["FR","RU","US"],"is_corresponding":true,"raw_author_name":"Victor Pambuccian","raw_affiliation_strings":["Integrative Studies, Arizona State University West, P.O. Box 37100, Phoenix, Arizona 85069\u20137100, U.S.A","The author would like to thank Prof. A NDREAS B LASS for his insistence on further simplifying the axiom system for CME , which was instrumental in arriving at the results of this paper","The author would like to thank Prof. ANDREAS BLASS for his insistence on further simplifying the axiom system for CME, which was instrumental in arriving at the results of this paper"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Integrative Studies, Arizona State University West, P.O. Box 37100, Phoenix, Arizona 85069\u20137100, U.S.A","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"The author would like to thank Prof. A NDREAS B LASS for his insistence on further simplifying the axiom system for CME , which was instrumental in arriving at the results of this paper","institution_ids":["https://openalex.org/I47431100"]},{"raw_affiliation_string":"The author would like to thank Prof. ANDREAS BLASS for his insistence on further simplifying the axiom system for CME, which was instrumental in arriving at the results of this paper","institution_ids":["https://openalex.org/I4210156717"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038599115"],"corresponding_institution_ids":["https://openalex.org/I4210156717","https://openalex.org/I47431100","https://openalex.org/I55732556"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":1.0118,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.78206953,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"41","issue":"3","first_page":"384","last_page":"394"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9984999895095825,"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/T12504","display_name":"Mathematics and Applications","score":0.9984999895095825,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9860000014305115,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9782999753952026,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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":0.799521803855896},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.7681381702423096},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.7651385068893433},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7521980404853821},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.6623783707618713},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6079384684562683},{"id":"https://openalex.org/keywords/non-euclidean-geometry","display_name":"Non-Euclidean geometry","score":0.5886902809143066},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37291568517684937},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3691069781780243},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3425569534301758},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32919415831565857},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3236180543899536},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11538437008857727}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.799521803855896},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.7681381702423096},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.7651385068893433},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7521980404853821},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.6623783707618713},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6079384684562683},{"id":"https://openalex.org/C10784197","wikidata":"https://www.wikidata.org/wiki/Q233858","display_name":"Non-Euclidean geometry","level":3,"score":0.5886902809143066},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37291568517684937},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3691069781780243},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3425569534301758},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32919415831565857},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3236180543899536},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11538437008857727},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19950410310","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19950410310","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W561473826","https://openalex.org/W628877253","https://openalex.org/W803752352","https://openalex.org/W1492786538","https://openalex.org/W1595469144","https://openalex.org/W1737043039","https://openalex.org/W1972305071","https://openalex.org/W1983384862","https://openalex.org/W1999988421","https://openalex.org/W2078569020","https://openalex.org/W2108569160","https://openalex.org/W2791136684","https://openalex.org/W4229873171","https://openalex.org/W4241429961","https://openalex.org/W4241659587","https://openalex.org/W4246268598"],"related_works":["https://openalex.org/W136616785","https://openalex.org/W2383246078","https://openalex.org/W1758527124","https://openalex.org/W1570186586","https://openalex.org/W2580237379","https://openalex.org/W4248394738","https://openalex.org/W4235340387","https://openalex.org/W4388311509","https://openalex.org/W4247078549","https://openalex.org/W2101247307"],"abstract_inverted_index":{"Abstract":[0],"In":[1,41],"this":[2],"paper":[3],"we":[4],"provide":[5],"quantifier\u2010free,":[6],"constructive":[7],"axiomatizations":[8,47],"for":[9],"several":[10],"fragments":[11],"of":[12],"plane":[13],"Euclidean":[14,17],"geometry":[15],"over":[16],"fields,":[18],"such":[19],"that":[20],"each":[21],"axiom":[22],"contains":[23],"at":[24,37],"most":[25,38],"4":[26],"variables.":[27],"The":[28],"languages":[29],"in":[30],"which":[31],"they":[32],"are":[33,48],"expressed":[34],"contain":[35],"only":[36],"ternary":[39],"operations.":[40],"some":[42],"precisely":[43],"defined":[44],"sense":[45],"these":[46],"the":[49],"simplest":[50],"possible.":[51]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}