• Corpus ID: 120671793

Jordan groups and homogeneous structures

  title={Jordan groups and homogeneous structures},
  author={David Bradley-Williams},
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 is transitive on Γ. Such sets Γ are called Jordan sets for G. Here we study infinite primitive Jordan groups which are automorphism groups of first order relational structures. We find a model theoretic application in classifying the reducts of an infinite family of semilinearly ordered partial… 

Jordan permutation groups and limits of 𝐷-relations

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

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



A survey of homogeneous structures

Jordan groups and limits of betweenness relations

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

Homogeneous Designs and Geometric Lattices

  • W. Kantor
  • Mathematics
    J. Comb. Theory, Ser. A
  • 1985

Ample Hierarchy

The ample hierarchy of geometries of stables theories is strict. We generalise the construction of the free pseudospace to higher dimensions and show that the n-dimensional free pseudospace is

Relations related to betweenness : their structure and automorphisms

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

Oligomorphic permutation groups

1. Introduction 2. Preliminaries 3. Examples and growth rates 4. Subgroups 5. Miscellaneous topics.