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Daniel Turetsky [9]Daniel D. Turetsky [3]
  1.  31
    Decidability and Computability of Certain Torsion-Free Abelian Groups.Rodney G. Downey, Sergei S. Goncharov, Asher M. Kach, Julia F. Knight, Oleg V. Kudinov, Alexander G. Melnikov & Daniel Turetsky - 2010 - Notre Dame Journal of Formal Logic 51 (1):85-96.
    We study completely decomposable torsion-free abelian groups of the form $\mathcal{G}_S := \oplus_{n \in S} \mathbb{Q}_{p_n}$ for sets $S \subseteq \omega$. We show that $\mathcal{G}_S$has a decidable copy if and only if S is $\Sigma^0_2$and has a computable copy if and only if S is $\Sigma^0_3$.
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  2.  9
    Computability-Theoretic Categoricity and Scott Families.Ekaterina Fokina, Valentina Harizanov & Daniel Turetsky - 2019 - Annals of Pure and Applied Logic 170 (6):699-717.
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  3.  31
    Two More Characterizations of K-Triviality.Noam Greenberg, Joseph S. Miller, Benoit Monin & Daniel Turetsky - 2018 - Notre Dame Journal of Formal Logic 59 (2):189-195.
    We give two new characterizations of K-triviality. We show that if for all Y such that Ω is Y-random, Ω is -random, then A is K-trivial. The other direction was proved by Stephan and Yu, giving us the first titular characterization of K-triviality and answering a question of Yu. We also prove that if A is K-trivial, then for all Y such that Ω is Y-random, ≡LRY. This answers a question of Merkle and Yu. The other direction is immediate, so (...)
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  4.  8
    Lowness for Effective Hausdorff Dimension.Steffen Lempp, Joseph S. Miller, Keng Meng Ng, Daniel D. Turetsky & Rebecca Weber - 2014 - Journal of Mathematical Logic 14 (2):1450011.
    We examine the sequences A that are low for dimension, i.e. those for which the effective dimension relative to A is the same as the unrelativized effective dimension. Lowness for dimension is a weakening of lowness for randomness, a central notion in effective randomness. By considering analogues of characterizations of lowness for randomness, we show that lowness for dimension can be characterized in several ways. It is equivalent to lowishness for randomness, namely, that every Martin-Löf random sequence has effective dimension (...)
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  5.  9
    S. S. Goncharov. Autostability and Computable Families of Constructivizations. Algebra and Logic, Vol. 14 , No. 6, Pp. 392–409. - S. S. Goncharov. The Quantity of Nonautoequivalent Constructivizations. Algebra and Logic, Vol. 16 , No. 3, Pp. 169–185. - S. S. Goncharov and V. D. Dzgoev. Autostability of Models. Algebra and Logic, Vol. 19 , No. 1, Pp. 28–37. - J. B. Remmel. Recursively Categorical Linear Orderings. Proceedings of the American Mathematical Society, Vol. 83 , No. 2, Pp. 387–391. - Terrence Millar. Recursive Categoricity and Persistence. The Journal of Symbolic Logic, Vol. 51 , No. 2, Pp. 430–434. - Peter Cholak, Segey Goncharov, Bakhadyr Khoussainov and Richard A. Shore. Computably Categorical Structures and Expansions by Constants. The Journal of Symbolic Logic, Vol. 64 , No. 1, Pp. 13–137. - Peter Cholak, Richard A. Shore and Reed Solomon. A Computably Stable Structure with No Scott Family of Finitary Formulas. Archive for Mathematical Logic, Vol. 45 , No. 5, Pp. 519–538. [REVIEW]Daniel Turetsky - 2012 - Bulletin of Symbolic Logic 18 (1):131-134.
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  6.  25
    Limitwise Monotonic Functions, Sets, and Degrees on Computable Domains.Asher M. Kach & Daniel Turetsky - 2010 - Journal of Symbolic Logic 75 (1):131-154.
    We extend the notion of limitwise monotonic functions to include arbitrary computable domains. We then study which sets and degrees are support increasing limitwise monotonic on various computable domains. As applications, we provide a characterization of the sets S with computable increasing η-representations using support increasing limitwise monotonic sets on ℚ and note relationships between the class of order-computable sets and the class of support increasing limitwise monotonic sets on certain domains.
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  7.  30
    Galvin’s “Racing Pawns” Game, Internal Hyperarithmetic Comprehension, and the Law of Excluded Middle.Chris Conidis, Noam Greenberg & Daniel Turetsky - 2013 - Notre Dame Journal of Formal Logic 54 (2):233-252.
    We show that the fact that the first player wins every instance of Galvin’s “racing pawns” game is equivalent to arithmetic transfinite recursion. Along the way we analyze the satisfaction relation for infinitary formulas, of “internal” hyperarithmetic comprehension, and of the law of excluded middle for such formulas.
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  8.  3
    Uniform Procedures in Uncountable Structures.Noam Greenberg, Alexander G. Melnikov, Julia F. Knight & Daniel Turetsky - 2018 - Journal of Symbolic Logic 83 (2):529-550.
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  9.  11
    Computability and Uncountable Linear Orders I: Computable Categoricity.Noam Greenberg, Asher M. Kach, Steffen Lempp & Daniel D. Turetsky - 2015 - Journal of Symbolic Logic 80 (1):116-144.
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  10.  10
    Computability and Uncountable Linear Orders II: Degree Spectra.Noam Greenberg, Asher M. Kach, Steffen Lempp & Daniel D. Turetsky - 2015 - Journal of Symbolic Logic 80 (1):145-178.
  11.  7
    Linear Orders Realized by C.E. Equivalence Relations.Ekaterina Fokina, Bakhadyr Khoussainov, Pavel Semukhin & Daniel Turetsky - 2016 - Journal of Symbolic Logic 81 (2):463-482.
  12. Several Papers Concerning Computable Categoricity.Daniel Turetsky - 2012 - Bulletin of Symbolic Logic 18 (1):131.