Axiomatic Theory of Betweenness
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2019
- DOI:
- 10.48550/arXiv.1902.00847
- arXiv:
- arXiv:1902.00847
- Bibcode:
- 2019arXiv190200847A
- Keywords:
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- Mathematics - Logic