{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:26:45Z","timestamp":1761611205350},"reference-count":17,"publisher":"Wiley","issue":"4","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 of metric\u2010Euclidean and of rectangular planes (generalizations of Euclidean planes). The languages in which the axiom systems are expressed contain three individual constants and two ternary operations. We also provide an axiom system in algorithmic logic for finite Euclidean planes, and for several minimal metric\u2010Euclidean planes. The axiom systems proposed will be used in a sequel to this paper to provide \u2018the simplest possible\u2019 axiom systems for several fragments of plane Euclidean geometry.<\/jats:p><jats:p><jats:bold>Mathematics Subject Classification:<\/jats:bold> 51M05, 51M15, 03F65.<\/jats:p>","DOI":"10.1002\/malq.19940400404","type":"journal-article","created":{"date-parts":[[2007,6,2]],"date-time":"2007-06-02T22:50:51Z","timestamp":1180824651000},"page":"455-477","source":"Crossref","is-referenced-by-count":9,"title":["Ternary Operations as Primitive Notions for Constructive Plane Geometry V"],"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":"10.1007\/BF01210963"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01210967"},{"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","doi-asserted-by":"publisher","DOI":"10.1007\/BF01540796"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01540797"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19480010404"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01448980"},{"key":"e_1_2_1_9_2","unstructured":"Karzel H. undH. J.Kroll Geschichte der Geometrie seit Hilbert. Wissenschaftliche Buchgesellschaft Darmstadt 1988."},{"key":"e_1_2_1_10_2","first-page":"531","article-title":"Rechtseitebenen und ihre Darstellung durch Integrit\u00e4tssysteme","volume":"10","author":"Karzel H.","year":"1979","journal-title":"Mitt. Math. Gesellschaft Hamburg"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19890350608"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19920380132"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19930390143"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19940400111"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69418-9"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01230121"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01223533"},{"key":"e_1_2_1_18_2","first-page":"1","article-title":"Beispiele invarianter Bewertungsringe und Rechtseitebenen","volume":"223","author":"Stanik R.","year":"1984","journal-title":"Ber. Math.\u2010Statist. Sekt. Forsch. Graz"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19940400404","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19940400404","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T16:14:29Z","timestamp":1695831269000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19940400404"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,1]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1994,1]]}},"alternative-id":["10.1002\/malq.19940400404"],"URL":"https:\/\/doi.org\/10.1002\/malq.19940400404","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]]}}}