Fra\"iss\'e Structures with Universal Automorphism Groups

TL;DR

This paper demonstrates that automorphism groups of certain Fra"iss"e structures with stationary independence are universal for automorphism groups of their substructures, including specific homogeneous n-gons.

Contribution

It establishes the universality of automorphism groups in Fra"iss"e structures with stationary independence, extending to some homogeneous n-gons.

Findings

Automorphism groups are universal for substructure automorphisms.

Applicable to certain homogeneous n-gons.

Provides a new framework for understanding automorphism group universality.

Abstract

We prove that the automorphism group of a Fra\"iss\'e structure M equipped with a notion of stationary independence is universal for the class of automorphism groups of substructures of M. Furthermore, we show that this applies to certain homogeneous n-gons.