A countably categorical structures of trees of D-sets

Asma Almazaydeh, University of Leeds. Part of the Models and sets seminar.

Asma Almazaydeh, University of Leeds
An ω-categorical structure of trees of D-sets

There are two classification theorems in the field of infinite primitive permutation Jordan groups.  One is by Adeleke and Neumann based on Cameron's classification of infinite permutation groups in 1976, and the second is by Adeleke and Macpherson in which they classified all infinite primitive permutation Jordan groups.  Such groups are highly transitive or preserve one of the linear-like structures, the tree-like structures, the Stiener systems as classified by Adeleke and Neumann or a limit of Stiener systems, B-relations or D-relations.  On the last two there are two non-isomorphic examples; the first one by Adeleke for a group preserves a limit of B- and D-relations, but it is not known weather it has an ω-categorical structure or not.  The second example is by Bhattacharjee and Macpherson for an ω-categorical structure and its automorphism group preserves a limit of betweenness relations.

I am working on an example of ω-categorical structure whose automorphism group  (hopefully) is a Jordan group preserves a limit of D-relations.

In the first part of the talk I will focus on the classification theorems, and in the second part I will explain the structure of trees of D-sets.