Jordan permutation groups and limits of D-relations

TL;DR

This paper constructs an $ ext{omega}$-categorical structure with an automorphism group that is an infinite oligomorphic Jordan primitive permutation group preserving a limit of D-relations, using Fra"issé amalgamation and semilinear orders.

Contribution

It introduces a novel construction of a structure with a specific automorphism group preserving a limit of D-relations, expanding understanding of Jordan permutation groups.

Findings

Constructed an $ ext{omega}$-categorical structure with the desired properties.

Demonstrated the preservation of a limit of D-relations by the automorphism group.

Established coherence conditions for the interrelation of D-sets.

Abstract

We construct via Fra\"iss\'e amalgamation an $\omega$-categorical structure whose automorphism group is an infinite oligomorphic Jordan primitive permutation group preserving a `limit of $D$-relations'. The construction is based on a semilinear order whose elements are labelled by sets carrying a $D$-relation, with strong coherence conditions governing how these $D$-sets are inter-related.