Isomorphism of Homogeneous Structures

@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}
}
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