Why did Euclid not need the Pasch axiom?

DOI10.1007/s00022-024-00712-xOpenAlexW4391898868MaRDI QIDQ6121100

Victor V. Pambuccian

Publication date: 26 February 2024

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

Full work available at URL: https://doi.org/10.1007/s00022-024-00712-x

zbMATH Keywords

axiom systemEuclidean geometrythe Pasch axiomEuclid's postulate V

Mathematics Subject Classification ID

Foundations of classical theories (including reverse mathematics) (03B30) Ordered geometries (ordered incidence structures, etc.) (51G05) Euclidean geometries (general) and generalizations (51M05)

Cites Work

• The axiomatics of ordered geometry: I. Ordered incidence spaces
• Ordered metric geometry
• Brouwer and Euclid
• Euklidische Geometrie ohne das Axiom von Pasch
• Ordered groups and ordered geometries
• Geometrien mit euklidischer Metrik, in denen es zu jeder Geraden durch einen nicht auf ihr liegenden Punkt mehrere Nichtschneidende gibt. I, II
• EUCLIDEAN TWO DIMENSIONAL, EQUIDISTANCE THEORY
• Concerning the order and the semi-order of n-dimensional Euclidean space
• CONSTRUCTIVE GEOMETRY AND THE PARALLEL POSTULATE
• A FORMAL SYSTEM FOR EUCLID’SELEMENTS
• Die Ordnungsfunktionen einer Geometrie
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