Zur Unabhängigkeit von Hilberts Axiomen des affinen Raumes
type: Item
instance of: scholarly article
title: Zur Unabhängigkeit von Hilberts Axiomen des affinen Raumes
zbMATH Open document ID: 0581.51001
DOI: 10.1007/BF01222941
author: Dieter Ruoff
published in: Journal of Geometry
publication date: 1985-01-01T00:00:00Z
review text: The aim of this article is to classify the incidence structures obtained in the following way: Assume that Hilbert's axioms, defining a classical affine space, are all satisfied except the uniqueness of the plane containing three given non-collinear points. Then, if the uniqueness of the plane is really not satisfied, such an incidence structure must be finite and, eliminating some entirely trivial variations, 39 models exist.
Mathematics Subject Classification ID: 51A15
Mathematics Subject Classification ID: 51Axx
zbMATH DE Number: 3929824
zbMATH Keywords: generalized spatial affine geometries
zbMATH Keywords: Hilbert's axioms
MaRDI profile type: Publication
cites work: Q3252280
cites work: The Two-Triangle Case of the Acquaintance Graph
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cites work: Q3286761
cites work: Das Parallelenaxiom im affinen Raum
cites work: Die Eindeutigkeit der Verbindungsebene im Raum
cites work: Q4088839
full work available at URL: https://doi.org/10.1007/bf01222941
OpenAlex ID: W2073260697
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description: scientific article; zbMATH DE number 3929824