On the axiomatics of projective and affine geometry in terms of line intersection

DOI10.1007/BF03322995zbMath1064.51001arXiv1304.0224OpenAlexW2044291282MaRDI QIDQ1885227

Hans Havlicek, Victor V. Pambuccian

Publication date: 28 October 2004

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.0224

zbMATH Keywords

affine spacesprojective spacesline geometry

Mathematics Subject Classification ID

General theory of linear incidence geometry and projective geometries (51A05) Homomorphism, automorphism and dualities in linear incidence geometry (51A10)

Related Items (5)

Coplanarity of lines in projective and polar Grassmann spaces ⋮ Possible primitive notions for geometry of spine spaces ⋮ Positive existential definability of parallelism in terms of betweenness in Archimedean ordered affine geometry ⋮ The ubiquitous axiom ⋮ Metric affine geometry on the universe of lines

Cites Work

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• Properties preserved under homomorphism
• On isomorphisms of Grassmann spaces
• Adjacency preserving transformations of Grassmann spaces
• On the geometry of algebraic homogeneous spaces
• Isomorphisms of Affine Pl\"ucker Spaces
• An Axiomatic Line Geometry

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