The conjugacy problem for automorphism groups of countable homogeneous structures

TL;DR

This paper investigates the complexity of the conjugacy problem in automorphism groups of various countable homogeneous structures, determining their exact Borel reducibility classifications.

Contribution

It provides the first precise complexity classifications of the conjugacy problem for automorphism groups of several countable homogeneous structures.

Findings

Determined the Borel complexity of conjugacy relations for multiple structures.

Established new benchmarks for the complexity of automorphism group conjugacy problems.

Provided a comprehensive analysis across different classes of homogeneous structures.

Abstract

We consider the conjugacy problem for the automorphism groups of a number of countable homogeneous structures. In each case we find the precise complexity of the conjugacy relation in the sense of Borel reducibility.