# On limits of betweenness relations

@inproceedings{BradleyWilliams2021OnLO, title={On limits of betweenness relations}, author={David Bradley-Williams and John Kenneth Truss}, year={2021} }

. 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¨ıss´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.

## References

SHOWING 1-10 OF 20 REFERENCES

### Jordan groups and limits of betweenness relations

- Mathematics
- 2006

Abstract A construction is given of an infinite primitive Jordan permutation group which preserves a ‘limit’ of betweenness relations. There is a previous construction due to Adeleke of a Jordan…

### Jordan permutation groups and limits of 𝐷-relations

- MathematicsJournal of Group Theory
- 2021

Abstract We construct via Fraïssé amalgamation an 𝜔-categorical structure whose automorphism group is an infinite oligomorphic Jordan primitive permutation group preserving a “limit of…

### Weak Fraisse categories

- Mathematics
- 2017

We develop the theory of weak Fraisse categories, where the crucial concept is the weak amalgamation property, discovered relatively recently in model theory. We show that, in a suitable framework,…

### Fraïssé’s Construction from a Topos-Theoretic Perspective

- MathematicsLogica Universalis
- 2014

A topos-theoretic interpretation of Fraïssé’s construction in Model Theory is presented, with applications to homogeneous models and countably categorical theories.

### Betweenness relations and cycle-free partial orders

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1996

The intuition behind the notion of a cycle-free partial order (CFPO) is that it should be a partial ordering (X, ≤ ) in which for any sequence of points (x0, x1;…, xn–1) with n ≤ 4 such that xi is…

### Jordan groups and homogeneous structures

- Mathematics
- 2014

A permutation group G acting transitively on a set Ω is a Jordan group if there is a proper subset Γ ⊂ Ω, subject to some non-triviality conditions, such that the pointwise stabiliser in G of Ω \ Γ…

### Relations related to betweenness : their structure and automorphisms

- Mathematics
- 1998

Preparation Semilinear order relations Abstract chain sets General betweenness relations Abstract direction sets Applications and commentary References.

### Universal domains and the amalgamation property

- MathematicsMathematical Structures in Computer Science
- 1993

A categorical generalization of a well-known result in model theory is used to characterize large classes of reasonable categories that contain universal homogeneous objects, and derives the existence and uniqueness of universal homogeneity domains for several categories of bifinite domains.

### On Irregular Infinite Jordan Groups

- Mathematics
- 2013

Two constructions are given of unfamiliar examples of infinite Jordan permutation groups. The examples are important to the classification of all infinite primitive Jordan groups. It is also shown…