{"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":1761611203914},"reference-count":14,"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":4699,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1994,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we provide a quantifier\u2010free constructive axiomatization for Euclidean planes in a first\u2010order language with only ternary operation symbols and three constant symbols (to be interpreted as \u2018points\u2019). We also determine the algorithmic theories of some \u2018naturally occurring\u2019 plane geometries.<\/jats:p><jats:p><jats:bold>Mathematics Subject Classification:<\/jats:bold> 03F65, 51M05, 51M15, 03B30.<\/jats:p>","DOI":"10.1002\/malq.19940400111","type":"journal-article","created":{"date-parts":[[2007,6,3]],"date-time":"2007-06-03T01:54:18Z","timestamp":1180835658000},"page":"76-86","source":"Crossref","is-referenced-by-count":7,"title":["Ternary Operations as Primitive Notions for Constructive Plane Geometry IV"],"prefix":"10.1002","volume":"40","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":"10.1002\/mana.19480010404"},{"key":"e_1_2_1_3_2","first-page":"77","article-title":"\u00dcber die Konstruierbarkeit mit Lineal, Rechtwinkelma\u00df und Eichma\u00df","volume":"1","author":"Bachmann F.","year":"1949","journal-title":"Math.\u2010Phys. Semesterber."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65537-1"},{"key":"e_1_2_1_5_2","first-page":"593","article-title":"Euclidean two dimensional equidistance theory","volume":"17","author":"Grochowska M.","year":"1984","journal-title":"Demonstratio Math."},{"key":"e_1_2_1_6_2","series-title":"Lecture Notes in Computer Science 2","first-page":"2","volume-title":"On the structure of algorithmic problems","author":"Engeler E.","year":"1973"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02950661"},{"key":"e_1_2_1_8_2","first-page":"143","article-title":"Quantifier\u2010free axioms for constructive plane geometry","volume":"20","author":"Moler N.","year":"1968","journal-title":"Compositio Math."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19890350608"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19920380132"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19930390143"},{"key":"e_1_2_1_12_2","unstructured":"Schnabel R. Euklidische Geometrie. Habilitationsschrift Universit\u00e4t Kiel 1981."},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01917574"},{"key":"e_1_2_1_14_2","volume-title":"Geometrie euklidischer Ebenen","author":"Schr\u00f6der E. M.","year":"1985"},{"key":"e_1_2_1_15_2","volume-title":"Algorithmische Theorien und konstruktive Geometrie","author":"Seeland H.","year":"1978"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19940400111","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19940400111","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T00:49:19Z","timestamp":1698108559000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19940400111"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,1]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1994,1]]}},"alternative-id":["10.1002\/malq.19940400111"],"URL":"https:\/\/doi.org\/10.1002\/malq.19940400111","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,1]]}}}