{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:26:43Z","timestamp":1761611203748},"reference-count":10,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":5064,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1993,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper continues the investigations begun in [6] and continued in [7] about quantifier\u2010free axiomatizations of plane Euclidean geometry using ternary operations. We show that plane Euclidean geometry over Archimedean ordered Euclidean fields can be axiomatized using only two ternary operations if one allows axioms that are not first\u2010order but universal <jats:italic>L<jats:sub>w1,w<\/jats:sub><\/jats:italic> sentences. The operations are: the transport of a segment on a halfline that starts at one of the endpoints of the given segment, and the operation which produces one of the intersection points of a perpendicular on a diameter of a circle (which intersects that diameter at a point inside the circle) with that circle. MSC: 03F65, 51M05, 51M15.<\/jats:p>","DOI":"10.1002\/malq.19930390143","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T17:19:33Z","timestamp":1180199973000},"page":"393-402","source":"Crossref","is-referenced-by-count":5,"title":["Ternary operations as primitive notions for constructive plane geometry III"],"prefix":"10.1002","volume":"39","author":[{"given":"Victor","family":"Pambuccian","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01705528"},{"key":"e_1_2_1_3_2","first-page":"64","volume-title":"Remarks on the theory of geometrical constructions. Lecture Notes in Mathematics","author":"Engeler E.","year":"1968"},{"key":"e_1_2_1_4_2","first-page":"2","volume-title":"On the structure of algorithmic problems. Lecture Notes in Computer Science","author":"Engeler E.","year":"1973"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-68929-1"},{"key":"e_1_2_1_6_2","unstructured":"Kijne D. Plane construction field theory. Ph.D. Thesis Utrecht 1956."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19890350608"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19920380132"},{"key":"e_1_2_1_9_2","volume-title":"Theorie der geometrischen Konstruktionen","author":"Schreiber P.","year":"1975"},{"key":"e_1_2_1_10_2","volume-title":"Algorithmische Theorien und konstruktive Geometrie","author":"Seeland H.","year":"1978"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00181213"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19930390143","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19930390143","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T20:59:56Z","timestamp":1698267596000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19930390143"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,1]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1993,1]]}},"alternative-id":["10.1002\/malq.19930390143"],"URL":"https:\/\/doi.org\/10.1002\/malq.19930390143","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,1]]}}}