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  1. Automorphisms of the lattice of recursively enumerable sets. Part II: Low sets.Robert I. Soare - 1982 - Annals of Mathematical Logic 22 (1):69.
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  • Conjectures and questions from Gerald Sacks's Degrees of Unsolvability.Richard A. Shore - 1997 - Archive for Mathematical Logic 36 (4-5):233-253.
    We describe the important role that the conjectures and questions posed at the end of the two editions of Gerald Sacks's Degrees of Unsolvability have had in the development of recursion theory over the past thirty years.
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  • Constructive Logic and the Medvedev Lattice.Sebastiaan A. Terwijn - 2006 - Notre Dame Journal of Formal Logic 47 (1):73-82.
    We study the connection between factors of the Medvedev lattice and constructive logic. The algebraic properties of these factors determine logics lying in between intuitionistic propositional logic and the logic of the weak law of the excluded middle (also known as De Morgan, or Jankov, logic). We discuss the relation between the weak law of the excluded middle and the algebraic notion of join-reducibility. Finally we discuss autoreducible degrees.
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  • Sets of real numbers closed under Turing equivalence: applications to fields, orders and automorphisms.Iván Ongay-Valverde - 2023 - Archive for Mathematical Logic 62 (5):843-869.
    In the first half of this paper, we study the way that sets of real numbers closed under Turing equivalence sit inside the real line from the perspective of algebra, measure and orders. Afterwards, we combine the results from our study of these sets as orders with a classical construction from Avraham to obtain a restriction about how non trivial automorphism of the Turing degrees (if they exist) interact with 1-generic degrees.
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  • Reducibility orderings: Theories, definability and automorphisms.Anil Nerode & Richard A. Shore - 1980 - Annals of Mathematical Logic 18 (1):61-89.
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  • Lattices of c-degrees.Robert S. Lubarsky - 1987 - Annals of Pure and Applied Logic 36:115-118.
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  • Local initial segments of the Turing degrees.Bjørn Kjos-Hanssen - 2003 - Bulletin of Symbolic Logic 9 (1):26-36.
    Recent results on initial segments of the Turing degrees are presented, and some conjectures about initial segments that have implications for the existence of nontrivial automorphisms of the Turing degrees are indicated.
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