Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 48, No. 2, pp. 399409 (2007) 

Orthogonality as single primitive notion for metric planesVictor PambuccianDepartment of Integrative Studies, Arizona State University  West Campus, Phoenix, AZ 850697100, U.S.A. email: pamb@math.west.asu.eduAbstract: We provide a first order axiomatization for Bachmann's metric planes in terms of points and the ternary relation $\perp$ with $\perp(abc)$ to be read as `$a, b, c$ are the vertices of a right triangle with right angle at $a$'. The axioms can be chosen to be $\forall\exists$statements. Classification (MSC2000): 51F15, 03B30 Full text of the article:
Electronic version published on: 7 Sep 2007. This page was last modified: 28 Jun 2010.
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