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  1. Samuel Coskey (2011). REVIEWS-S. Gao, Invariant Descriptive Set Theory. Bulletin of Symbolic Logic 17 (2):265.
     
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  2. Samuel Coskey, Paul Ellis & Scott Schneider (2011). The Conjugacy Problem for the Automorphism Group of the Random Graph. Archive for Mathematical Logic 50 (1):215-221.
    We prove that the conjugacy problem for the automorphism group of the random graph is Borel complete, and discuss the analogous problem for some other countably categorical structures.
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  3. Samuel Coskey (2010). Borel Reductions of Profinite Actions Of. Annals of Pure and Applied Logic 161 (10):1270-1279.
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  4. Samuel Coskey & Joel David Hamkins (2010). Infinite Time Decidable Equivalence Relation Theory. Notre Dame Journal of Formal Logic 52 (2):203-228.
    We introduce an analogue of the theory of Borel equivalence relations in which we study equivalence relations that are decidable by an infinite time Turing machine. The Borel reductions are replaced by the more general class of infinite time computable functions. Many basic aspects of the classical theory remain intact, with the added bonus that it becomes sensible to study some special equivalence relations whose complexity is beyond Borel or even analytic. We also introduce an infinite time generalization of the (...)
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  5. Samuel Coskey & Roman Kossak (2010). The Complexity of Classification Problems for Models of Arithmetic. Bulletin of Symbolic Logic 16 (3):345-358.
    We observe that the classification problem for countable models of arithmetic is Borel complete. On the other hand, the classification problems for finitely generated models of arithmetic and for recursively saturated models of arithmetic are Borel; we investigate the precise complexity of each of these. Finally, we show that the classification problem for pairs of recursively saturated models and for automorphisms of a fixed recursively saturated model are Borel complete.
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