We show that for any countable homogeneous ordered graph G, the conjugacy problem for automorphisms of G is Borel complete. In fact we establish that each such G satisfies a strong extension property called ABAP, which implies that the isomorphism relation on substructures of G is Borel reducible to the conjugacy relation on automorphisms of G.
This is a post-peer-review, pre-copyedit version of an article published in Archive for Mathematical Logic. The final authenticated version is available online at doi: 10.1007/s00153-018-0645-0
Coskey, Samuel and Ellis, Paul. (2019). "Conjugacy for Homogeneous Ordered Graphs". Archive for Mathematical Logic, 58(3-4), 457-467. https://doi.org/10.1007/s00153-018-0645-0