Binary relations as single primitive notions for hyperbolic three-space and the inversive plane.

DOI10.1016/S0019-3577(00)80027-0zbMath1044.51012MaRDI QIDQ5951549

Victor V. Pambuccian

Publication date: 2000

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Metric geometry (51F99) Möbius geometries (51B10)

Related Items (3)

Positive existential definability of parallelism in terms of betweenness in Archimedean ordered affine geometry ⋮ Mappings preserving the area equality of hyperbolic triangles are motions ⋮ Sphere tangency as single primitive notion for hyperbolic and Euclidean geometry

Cites Work

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• Simplicity
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• A Beckman-Quarles Type Theorem for Coxeter's Inversive Distance
• Relations on lines as primitive notions for Euclidean geometry
• A logical look at characterizations of geometric transformations under mild hypotheses
• On orthogonality-preserving Plücker transformations of hyperbolic spaces

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