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@article{Clemens2009IsomorphismOH, title={Isomorphism of Homogeneous Structures}, author={John D. Clemens}, journal={Notre Dame Journal of Formal Logic}, year={2009}, volume={50}, pages={1-22} }

- Published 2009 in Notre Dame Journal of Formal Logic
DOI:10.1215/00294527-2008-024

We consider the complexity of the isomorphism relation on countable first-order structures with transitive automorphism groups. We use the theory of Borel reducibility of equivalence relations to show that the isomorphism problem for vertex-transitive graphs is as complicated as the isomorphism problem for arbitrary graphs, and determine for which first-order languages the isomorphism problem for transitive countable structures is as complicated as it is for arbitrary countable structures. We… CONTINUE READING