Positive existential definability of parallelism in terms of betweenness in Archimedean ordered affine geometry
type: Item
instance of: scholarly article
title: Positive existential definability of parallelism in terms of betweenness in Archimedean ordered affine geometry
zbMATH Open document ID: 1230.51013
DOI: 10.1216/RMJ-2011-41-5-1501
published in: Rocky Mountain Journal of Mathematics
publication date: 2011-10-18T00:00:00Z
review text: The authors show that in Archimedean ordered affine planes, parallelism is positively existentially definable in terms of betweenness and negation of equality. This can be used to prove the following result of \textit{X.-D. Hou} and \textit{G. McColm} [Rocky Mt. J. Math. 38, No. 1, 123--137 (2008; Zbl 1167.26004)]: every self-map of an Archimedean ordered pappian affine plane preserving betweenness in both directions is surjective.
reviewed by: Theo Grundhöfer
Mathematics Subject Classification ID: 51G05
Mathematics Subject Classification ID: 03C65
Mathematics Subject Classification ID: 51F20
Mathematics Subject Classification ID: 51F05
zbMATH DE Number: 5959795
zbMATH Keywords: Archimedean ordered plane
zbMATH Keywords: definability
author: Franz B. Kalhoff
author: Victor V. Pambuccian
MaRDI profile type: Publication
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full work available at URL: rmj-2011-41-5-1501
OpenAlex ID: W1995322945
description: scientific article; zbMATH DE number 5959795