On limits of betweenness relations

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.