{"id":"https://openalex.org/W1972305071","doi":"https://doi.org/10.1002/malq.19920380132","title":"TERNARY OPERATIONS AS PRIMITIVE NOTIONS FOR PLANE GEOMETRY II","display_name":"TERNARY OPERATIONS AS PRIMITIVE NOTIONS FOR PLANE GEOMETRY II","publication_year":1992,"publication_date":"1992-01-01","ids":{"openalex":"https://openalex.org/W1972305071","doi":"https://doi.org/10.1002/malq.19920380132","mag":"1972305071"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19920380132","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19920380132","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/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Victor Pambuccian","raw_affiliation_strings":["University of Michigan Department of Mathematics Ann Arbor, MI 48109-1003, U.S.A","University of Michigan Department of Mathematics Ann Arbor, MI 48109\u20101003, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Michigan Department of Mathematics Ann Arbor, MI 48109-1003, U.S.A","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"University of Michigan Department of Mathematics Ann Arbor, MI 48109\u20101003, U.S.A","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038599115"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":1.913,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.84589453,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":"1","first_page":"345","last_page":"348"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9919999837875366,"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":0.9919999837875366,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9894000291824341,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9836000204086304,"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/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.8484456539154053},{"id":"https://openalex.org/keywords/pythagorean-triple","display_name":"Pythagorean triple","score":0.772717297077179},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.7363394498825073},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7334810495376587},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7022930383682251},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6276109218597412},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.5314022302627563},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4886375069618225},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36130470037460327},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3412593603134155},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2749899625778198},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12626060843467712},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.08966511487960815}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.8484456539154053},{"id":"https://openalex.org/C80918210","wikidata":"https://www.wikidata.org/wiki/Q208225","display_name":"Pythagorean triple","level":3,"score":0.772717297077179},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.7363394498825073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7334810495376587},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7022930383682251},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6276109218597412},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.5314022302627563},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4886375069618225},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36130470037460327},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3412593603134155},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2749899625778198},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12626060843467712},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08966511487960815}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19920380132","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19920380132","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":1,"referenced_works":["https://openalex.org/W4229873171"],"related_works":["https://openalex.org/W3038906685","https://openalex.org/W2392975301","https://openalex.org/W2259363500","https://openalex.org/W2387543012","https://openalex.org/W2620974800","https://openalex.org/W4287077343","https://openalex.org/W2368479431","https://openalex.org/W4297809691","https://openalex.org/W3182949439","https://openalex.org/W2994801930"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"proved":[2],"in":[3,19],"the":[4],"first":[5],"part":[6],"[1]":[7],"that":[8,38],"plane":[9],"geometry":[10],"over":[11],"Pythagorean":[12],"fields":[13],"is":[14],"axiomatizable":[15],"by":[16],"quantifier\u2010free":[17],"axioms":[18],"a":[20],"language":[21],"with":[22],"three":[23,29],"individual":[24],"constants,":[25],"one":[26],"binary":[27],"and":[28],"ternary":[30],"operation":[31,42],"symbols.":[32],"In":[33],"this":[34],"paper":[35],"we":[36],"prove":[37],"two":[39],"of":[40],"these":[41],"symbols":[43],"are":[44],"superfluous.":[45]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}