On limits of betweenness relations

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.