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  1. An effectively closed set with no join property.Ahmet Çevik - 2021 - Mathematical Logic Quarterly 67 (3):313-320.
    In this paper, we establish a relationship between the join property and Turing degrees of members of effectively closed sets in Cantor space, i.e., classes. We first give a proof of the observation that there exists a non‐empty special class in which no join of two members computes the halting set. We then prove the existence of a non‐empty special class such that no member satisfies the join property, where a degree satisfies the join property if for all non‐zero there (...)
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  • Π 1 0 Classes, Peano Arithmetic, Randomness, and Computable Domination.David E. Diamondstone, Damir D. Dzhafarov & Robert I. Soare - 2010 - Notre Dame Journal of Formal Logic 51 (1):127-159.
    We present an overview of the topics in the title and of some of the key results pertaining to them. These have historically been topics of interest in computability theory and continue to be a rich source of problems and ideas. In particular, we draw attention to the links and connections between these topics and explore their significance to modern research in the field.
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