On a splitting of the parallel postulate

DOI10.1007/s00022-022-00626-6zbMath1489.51005OpenAlexW4206925831MaRDI QIDQ2668175

Victor V. Pambuccian

Publication date: 3 March 2022

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-022-00626-6

zbMATH Keywords

parallel postulateordered geometrymetric-Euclidean planes\textit{Lotschnittaxiom}

Mathematics Subject Classification ID

Foundations of classical theories (including reverse mathematics) (03B30) Ordered geometries (ordered incidence structures, etc.) (51G05) Absolute planes in metric geometry (51F05)

Cites Work

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• Ordered metric geometry
• The ubiquitous axiom
• Ordered groups and ordered geometries
• Orthogonality as single primitive notion for metric planes
• Eine absolute Axiomatik der Geometrie in einer begrenzten Ebene
• Geometrien mit euklidischer Metrik, in denen es zu jeder Geraden durch einen nicht auf ihr liegenden Punkt mehrere nichtschneidende gibt. I, II
• Metamathematical discussion of some affine geometries

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