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  1. Chris Conidis, Noam Greenberg & Daniel Turetsky (2013). Galvin's “Racing Pawns” Game, Internal Hyperarithmetic Comprehension, and the Law of Excluded Middle. Notre Dame Journal of Formal Logic 54 (2):233-252.
    We show that the fact that the first player (“white”) wins every instance of Galvin’s “racing pawns” game (for countable trees) 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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  2. Daniel Turetsky (2012). Several Papers Concerning Computable Categoricity. Bulletin of Symbolic Logic 18 (1):131.
     
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  3. Rodney G. Downey, Sergei S. Goncharov, Asher M. Kach, Julia F. Knight, Oleg V. Kudinov, Alexander G. Melnikov & Daniel Turetsky (2010). Decidability and Computability of Certain Torsion-Free Abelian Groups. 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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  4. Asher M. Kach & Daniel Turetsky (2010). Limitwise Monotonic Functions, Sets, and Degrees on Computable Domains. 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 (support strictly 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 ${\Bbb Q}$ and note relationships between the class of order-computable sets and the class of support increasing (support strictly increasing) limitwise monotonic sets on certain domains.
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