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An axiomatics for hyperbolic projective-metric planes in terms of lines and orthogonality. (English) Zbl 1101.51007

The starting point of this paper is Lingenberg’s partly group theoretic, partly geometric system of axioms for hyperbolic projective-metric planes [R. Lingenberg, Metric planes and metric vector spaces. Pure and Applied Mathematics. A Wiley-Interscience Publication. New York etc.: John Whiley & Sons. (1979; Zbl 0419.51001)].
The author shows that these planes are axiomatizable in terms of lines and orthogonality.

MSC:

51M10 Hyperbolic and elliptic geometries (general) and generalizations
03B30 Foundations of classical theories (including reverse mathematics)

Citations:

Zbl 0419.51001
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