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arXiv · 1902.00847

Axiomatic Theory of Betweenness

Sanaz Azimipour·Pavel Naumov
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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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Sanaz Azimipour, Pavel Naumov. 2019-02-03. Axiomatic Theory of Betweenness. https://arxiv.org/abs/1902.00847

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