Simplicity of the automorphism groups of some binary homogeneous structures determined by triangle constraints

TL;DR

This paper proves the simplicity of automorphism groups for certain binary homogeneous structures defined by triangle constraints, using stationary independence relations.

Contribution

It establishes the simplicity of automorphism groups for specific structures via new application of stationary independence relations.

Findings

Automorphism groups are simple for these structures.

Uses stationary independence relations to analyze automorphism groups.

Extends understanding of symmetry in binary homogeneous structures.

Abstract

We study some amalgamation classes introduced by Cherlin and prove the simplicity of the automorphism groups of the Fra{\"\i}ss{\'e} limits of these classes. We employ the machinery of stationary independence relations used by Tent and Ziegler.