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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.

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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

Available for download on Friday, May 01, 2020

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