Isomorphism of Homogeneous Structures

Notre Dame Journal of Formal Logic 50 (1):1-22 (2009)
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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 then use these results to characterize the complexity of the isometry relation for certain classes of homogeneous and ultrahomogeneous metric spaces



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Isometry of Polish metric spaces.John D. Clemens - 2012 - Annals of Pure and Applied Logic 163 (9):1196-1209.

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Stability of nilpotent groups of class 2 and prime exponent.Alan H. Mekler - 1981 - Journal of Symbolic Logic 46 (4):781-788.

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