Axiom systems implying infinity in the foundations of geometry

DOI10.1007/s13366-020-00532-5zbMath1473.51012OpenAlexW3092412719WikidataQ114017087 ScholiaQ114017087MaRDI QIDQ2022359

Rolf Struve, Victor V. Pambuccian

Publication date: 29 April 2021

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13366-020-00532-5

zbMATH Keywords

axiom systemhyperbolic geometryinfinityordered geometrymetric planes

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Ordered geometries (ordered incidence structures, etc.) (51G05) Absolute planes in metric geometry (51F05)

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Cites Work

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• Finite Cayley-Klein geometries.
• Zur Abhängigkeit von Anordnungsaxiomen. (On relations between axioms of betweenness)
• Klassifizierung von Halbordnungen. (On classifications of halforderings)
• Zur spiegelungsgeometrischen Begründung von Geometrien
• Non-Euclidean incidence planes
• Eine algebraische Beschreibung der metrischen Ebenen mit ineinander beweglichen Geraden
• Eine Kennzeichnung der Gruppe der gebrochen-linearen Transformationen
• Forms of the Pasch axiom in ordered geometry

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