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Axiomatic theory of betweenness

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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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Authors and Affiliations

  1. Berlin University of Applied Sciences, Berlin, Germany

    Sanaz Azimipour

  2. Tulane University, New Orleans, LA, USA

    Pavel Naumov

Authors
  1. Sanaz Azimipour
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  2. Pavel Naumov
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Correspondence to Pavel Naumov.

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Azimipour, S., Naumov, P. Axiomatic theory of betweenness. Arch. Math. Logic 60, 227–239 (2021). https://doi.org/10.1007/s00153-020-00744-5

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  • DOI: https://doi.org/10.1007/s00153-020-00744-5

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