On the simplicity of ordered geometry

DOI10.1007/s00022-013-0155-5zbMath1280.51007OpenAlexW1992001715MaRDI QIDQ1956325

Victor V. Pambuccian

Publication date: 13 June 2013

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

Full work available at URL: https://doi.org/10.1007/s00022-013-0155-5

zbMATH Keywords

simplicityPasch axiomsplitting an axiomordered planesinner and outer form of the Pasch axiomPasch's theorem

Mathematics Subject Classification ID

Axiomatic and generalized convexity (52A01) Foundations of classical theories (including reverse mathematics) (03B30) Ordered geometries (ordered incidence structures, etc.) (51G05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The axiomatics of ordered geometry: I. Ordered incidence spaces
• The simplest axiom system for plane hyperbolic geometry revisited
• Another splitting of the Pasch axiom
• Weakly ordered plane geometry
• Simplicity
• A proof of Pasch's axiom in the absolute theory of oriented parallelity
• The simplest axiom system for plane hyperbolic geometry
• The non-planarity of \(K_{5}\) and \(K_{3,3}\) as axioms for plane ordered geometry
• Eine Bemerkung zum Axiom von Pasch in Hilberts 'Grundlagen der Geometrie'
• Forms of the Pasch axiom in ordered geometry
• Concerning the order and the semi-order of n-dimensional Euclidean space
• Euclidean and Non-Euclidean Geometries Without Continuity
• Ternary Operations as Primitive Notions for Constructive Plane Geometry VI

This page was built for publication: On the simplicity of ordered geometry