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Daniel Turetsky [10]Dan Turetsky [5]Daniel D. Turetsky [3]
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  1.  16
    Computing K-Trivial Sets by Incomplete Random Sets.Laurent Bienvenu, Adam R. Day, Noam Greenberg, Antonín Kučera, Joseph S. Miller, André Nies & Dan Turetsky - 2014 - Bulletin of Symbolic Logic 20 (1):80-90.
    EveryK-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Martin-Löf random set that does not compute the halting problem.
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  2.  11
    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.
    LetEbe a computably enumerable equivalence relation on the setωof natural numbers. We say that the quotient set$\omega /E$realizesa linearly ordered set${\cal L}$if there exists a c.e. relation ⊴ respectingEsuch that the induced structure is isomorphic to${\cal L}$. Thus, one can consider the class of all linearly ordered sets that are realized by$\omega /E$; formally,${\cal K}\left = \left\{ {{\cal L}\,|\,{\rm{the}}\,{\rm{order}}\, - \,{\rm{type}}\,{\cal L}\,{\rm{is}}\,{\rm{realized}}\,{\rm{by}}\,E} \right\}$. In this paper we study the relationship between computability-theoretic properties ofEand algebraic properties of linearly ordered sets realized (...)
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  3.  8
    Strong Jump-Traceability.Noam Greenberg & Dan Turetsky - 2018 - Bulletin of Symbolic Logic 24 (2):147-164.
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  4.  11
    Characterizing Lowness for Demuth Randomness.Laurent Bienvenu, Rod Downey, Noam Greenberg, André Nies & Dan Turetsky - 2014 - Journal of Symbolic Logic 79 (2):526-560.
    We show the existence of noncomputable oracles which are low for Demuth randomness, answering a question in [15]. We fully characterize lowness for Demuth randomness using an appropriate notion of traceability. Central to this characterization is a partial relativization of Demuth randomness, which may be more natural than the fully relativized version. We also show that an oracle is low for weak Demuth randomness if and only if it is computable.
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  5.  43
    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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  6.  31
    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.  16
    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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  8.  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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  9.  3
    Punctual Categoricity and Universality.Rod Downey, Noam Greenberg, Alexander Melnikov, Keng Meng Ng & Daniel Turetsky - forthcoming - Journal of Symbolic Logic:1-31.
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  10.  1
    Relationships Between Computability‐Theoretic Properties of Problems.Rod Downey, Noam Greenberg, Matthew Harrison‐Trainor, Ludovic Patey & Dan Turetsky - forthcoming - Journal of Symbolic Logic:1-26.
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  11.  11
    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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  12.  12
    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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  13.  14
    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.
  14.  55
    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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  15.  5
    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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  16.  2
    Coding in the Automorphism Group of a Computably Categorical Structure.Dan Turetsky - 2020 - Journal of Mathematical Logic 20 (3):2050016.
    Using new techniques for controlling the categoricity spectrum of a structure, we construct a structure with degree of categoricity but infinite spectral dimension, answering a question of Bazhenov, Kalimullin and Yamaleev. Using the same techniques, we construct a computably categorical structure of non-computable Scott rank.
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  17. Several Papers Concerning Computable Categoricity.Daniel Turetsky - 2012 - Bulletin of Symbolic Logic 18 (1):131.
  18.  90
    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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