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Axiomatic Theory of Betweenness

Axiomatic Theory of Betweenness
Axiomatic Theory of Betweenness
Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three sets of points. The main technical result is a sound and complete logical system describing universal properties of this relation between sets of vertices of a graph.
Axiomatization, Betweenness, Completeness theorem
0933-5846
227-239
Azimipour, Sanaz
b6f3cca5-3fc1-43e3-9c2d-2f87409a37ee
Naumov, Pavel
8b6c40fb-b199-44d5-a8e2-0ebd021566b0
Azimipour, Sanaz
b6f3cca5-3fc1-43e3-9c2d-2f87409a37ee
Naumov, Pavel
8b6c40fb-b199-44d5-a8e2-0ebd021566b0

Azimipour, Sanaz and Naumov, Pavel (2021) Axiomatic Theory of Betweenness. Archive for Mathematical Logic, 60 (1-2), 227-239. (doi:10.1007/s00153-020-00744-5).

Record type: Article

Abstract

Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three sets of points. The main technical result is a sound and complete logical system describing universal properties of this relation between sets of vertices of a graph.

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More information

Accepted/In Press date: 3 July 2020
e-pub ahead of print date: 13 July 2020
Published date: 1 February 2021
Keywords: Axiomatization, Betweenness, Completeness theorem

Identifiers

Local EPrints ID: 452124
URI: http://eprints.soton.ac.uk/id/eprint/452124
ISSN: 0933-5846
PURE UUID: 9accc0cf-8db0-47c6-84cf-978f06287435
ORCID for Pavel Naumov: ORCID iD orcid.org/0000-0003-1687-045X

Catalogue record

Date deposited: 25 Nov 2021 16:46
Last modified: 26 Nov 2021 03:25

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Contributors

Author: Sanaz Azimipour
Author: Pavel Naumov ORCID iD

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