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  1.  20
    Infinite Time Decidable Equivalence Relation Theory.Samuel Coskey & Joel David Hamkins - 2011 - 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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  2.  29
    The Complexity of Classification Problems for Models of Arithmetic.Samuel Coskey & Roman Kossak - 2010 - 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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  3.  11
    The Conjugacy Problem for the Automorphism Group of the Random Graph.Samuel Coskey, Paul Ellis & Scott Schneider - 2011 - 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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  4.  5
    Borel Reductions of Profinite Actions Of.Samuel Coskey - 2010 - Annals of Pure and Applied Logic 161 (10):1270-1279.
    Greg Hjorth and Simon Thomas proved that the classification problem for torsion-free abelian groups of finite rank strictly increases in complexity with the rank. Subsequently, Thomas proved that the complexities of the classification problems for p-local torsion-free abelian groups of fixed rank n are pairwise incomparable as p varies. We prove that if 3≤m (...)
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  5. G. A. Elliott, I. Farah, V. I. Paulsen, C. Rosendal, A. S. Toms, and A. Törnquist. The Isomorphism Relation for Separable C*-Algebras. Mathematics Research Letters, Vol. 20 , No. 6, Pp. 1071–1080.Marcin Sabok. Completeness of the Isomorphism Problem for Separable C*-Algebras. Inventiones Mathematicae, to Appear, Published Online at Link.Springer.Com/Journal/222. [REVIEW]Samuel Coskey - 2015 - Bulletin of Symbolic Logic 21 (4):427-430.
  6. REVIEWS-S. Gao, Invariant Descriptive Set Theory.Samuel Coskey - 2011 - Bulletin of Symbolic Logic 17 (2):265.
     
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