Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 48, No. 2, pp. 399-409 (2007)

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Orthogonality as single primitive notion for metric planes

Victor Pambuccian

Department of Integrative Studies, Arizona State University -- West Campus, Phoenix, AZ 85069-7100, U.S.A. e-mail:

Abstract: 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

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Electronic version published on: 7 Sep 2007. This page was last modified: 28 Jun 2010.

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