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  1.  39
    The Conjugacy Problem for the Automorphism Group of the Random Graph.Samuel Coskey, Paul Ellis & Scott Schneider - 2011 - Archive for Mathematical Logic 50 (1-2):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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  2.  38
    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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  3.  1
    The Conjugacy Problem for Automorphism Groups of Countable Homogeneous Structures.Samuel Coskey & Paul Ellis - 2016 - Mathematical Logic Quarterly 62 (6):580-589.
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  4.  56
    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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  5.  10
    On the Classification of Vertex-Transitive Structures.John Clemens, Samuel Coskey & Stephanie Potter - 2019 - Archive for Mathematical Logic 58 (5-6):565-574.
    We consider the classification problem for several classes of countable structures which are “vertex-transitive”, meaning that the automorphism group acts transitively on the elements. We show that the classification of countable vertex-transitive digraphs and partial orders are Borel complete. We identify the complexity of the classification of countable vertex-transitive linear orders. Finally we show that the classification of vertex-transitive countable tournaments is properly above \ in complexity.
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  6.  4
    The Classification of Countable Models of Set Theory.John Clemens, Samuel Coskey & Samuel Dworetzky - 2020 - Mathematical Logic Quarterly 66 (2):182-189.
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  7.  8
    Cardinal Characteristics and Countable Borel Equivalence Relations.Samuel Coskey & Scott Schneider - 2017 - Mathematical Logic Quarterly 63 (3-4):211-227.
    Boykin and Jackson recently introduced a property of countable Borel equivalence relations called Borel boundedness, which they showed is closely related to the union problem for hyperfinite equivalence relations. In this paper, we introduce a family of properties of countable Borel equivalence relations which correspond to combinatorial cardinal characteristics of the continuum in the same way that Borel boundedness corresponds to the bounding number math formula. We analyze some of the basic behavior of these properties, showing, e.g., that the property (...)
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  8.  10
    Conjugacy for Homogeneous Ordered Graphs.Samuel Coskey & Paul Ellis - 2019 - Archive for Mathematical Logic 58 (3-4):457-467.
    We show that for any countable homogeneous ordered graph G, the conjugacy problem for automorphisms of G is Borel complete. In fact we establish that each such G satisfies a strong extension property called ABAP, which implies that the isomorphism relation on substructures of G is Borel reducible to the conjugacy relation on automorphisms of G.
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  9.  19
    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.
  10.  14
    Su Gao. Invariant Descriptive Set Theory. Pure and Applied Mathematics. Chapman & Hall/CRC, Boca Raton, 2009, Xiv + 392 Pp. [REVIEW]Samuel Coskey - 2011 - Bulletin of Symbolic Logic 17 (2):265-267.