On limits of betweenness relations
David Bradley-Williams, John K Truss

TL;DR
This paper introduces a versatile method for constructing limits of betweenness relations, unifying previous approaches and extending their applicability through the use of trees of B-sets.
Contribution
It provides a generalized framework for limits of betweenness relations, integrating and extending prior methods by Adeleke and Bhattacharjee and Macpherson.
Findings
Unified construction method for limits of betweenness relations
Extension of the tree of B-sets concept to broader classes
Connections between different approaches to betweenness limits
Abstract
We give a flexible method for constructing a wide variety of limits of betweenness relations. This unifies work of Adeleke, who constructed a Jordan group preserving a limit of betweenness relations, and Bhattacharjee and Macpherson who gave an alternative method using a Fra\"ss\'e-type construction. A key ingredient in their work is the notion of a tree of B-sets. We employ this, and extend its use to a wider class of examples.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Algebra and Logic · Rough Sets and Fuzzy Logic
