A logical look at characterizations of geometric transformations under mild hypotheses

DOI10.1016/S0019-3577(00)80009-9zbMath0987.51010MaRDI QIDQ5935915

Victor V. Pambuccian

Publication date: 28 June 2001

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

zbMATH Keywords

orthogonalitycharacterization of geometric transformations under mild hypothesescirclesEuclidean geometryMiquelian Möbius geometrymodel theoretic counterpart

Mathematics Subject Classification ID

Euclidean geometries (general) and generalizations (51M05) Interpolation, preservation, definability (03C40) Möbius geometries (51B10)

Related Items (11)

Axiomatizations of Euclidean geometry in terms of points, equilateral triangles or squares, and incidence. ⋮ Linear mappings approximately preserving \(\rho_\ast\)-orthogonality ⋮ On Exact and Approximate Orthogonalities Based on Norm Derivatives ⋮ Positive existential definability of parallelism in terms of betweenness in Archimedean ordered affine geometry ⋮ Lambert or Saccheri quadrilaterals as single primitive notions for plane hyperbolic geometry ⋮ Mappings preserving the area equality of hyperbolic triangles are motions ⋮ Linear mappings approximately preserving orthogonality ⋮ Binary relations as single primitive notions for hyperbolic three-space and the inversive plane. ⋮ Sphere tangency as single primitive notion for hyperbolic and Euclidean geometry ⋮ On bijections that preserve complementarity of subspaces ⋮ On Automorphisms of Flag Spaces

Cites Work

• Über den Begriff der Orthogonalität in der Kreisgeometrie
• Properties preserved under homomorphism
• Bijections of \({\mathbb{R}}^ n\) onto itself
• Zur Kennzeichnung Fanoscher affin-metrischer Geometrien
• How to keep the quadrilateral inscribed
• Theory of models with generalized atomic formulas
• On the characterization of plane projective and complex MOEBIUS‐transformations
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