The axiomatics of ordered geometry: I. Ordered incidence spaces
type: Item
instance of: scholarly article
title: The axiomatics of ordered geometry: I. Ordered incidence spaces
zbMATH Open document ID: 1227.51010
author: Victor V. Pambuccian
published in: Expositiones Mathematicae
publication date: 2011-05-02T00:00:00Z
review text: The author presents a survey of the development of the axiomatic theory of ordered and half-ordered incidence geometry, starting from \textit{M. Pasch}'s book [Vorlesungen über neuere Geometrie. Leipzig. Teubner (1882; JFM 14.0498.01)]. For reasons of comparability, the different axiom systems are transferred into one common language, namely first-order logic. Only in the case of Archimedian ordered geometry extensions of first-order logic are needed. The paper contains a wealth of information, and it will certainly become a standard reference in the field. Particularly valuable is the bibliography which contains 358 entries and appears to be rather complete.
reviewed by: Norbert Knarr
Mathematics Subject Classification ID: 51G05
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 52A01
Mathematics Subject Classification ID: 03B30
zbMATH DE Number: 5882933
zbMATH Keywords: ordered geometry
zbMATH Keywords: axiom system
zbMATH Keywords: half-ordered geometry
zbMATH Keywords: Pasch axiom
MaRDI profile type: Publication
full work available at URL: j.exmath.2010.09.004
OpenAlex ID: W2203508461
Wikidata QID: Q56639408
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The axiomatics of ordered geometry: I. Ordered incidence spaces (DOI)
DOI: 10.1016/J.EXMATH.2010.09.004