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  1. Diagonals and semihyperhypersimple sets.Martin Kummer - 1991 - Journal of Symbolic Logic 56 (3):1068-1074.
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  • Diagonals and Semihyperhypersimple Sets.Martin Kummer - 1991 - Journal of Symbolic Logic 56 (3):1068-1074.
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  • Diagonals and d-maximal sets.Eberhard Herrmann & Martin Kummer - 1994 - Journal of Symbolic Logic 59 (1):60-72.
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  • Diagonals and $mathscr{D}$-Maximal Sets.Eberhard Herrmann & Martin Kummer - 1994 - Journal of Symbolic Logic 59 (1):60-72.
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  • Codable sets and orbits of computably enumerable sets.Leo Harrington & Robert I. Soare - 1998 - Journal of Symbolic Logic 63 (1):1-28.
    A set X of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. Let ε denote the structure of the computably enumerable sets under inclusion, $\varepsilon = (\{W_e\}_{e\in \omega}, \subseteq)$ . We previously exhibited a first order ε-definable property Q(X) such that Q(X) guarantees that X is not Turing complete (i.e., does not code complete information about c.e. sets). Here we show first that Q(X) implies that X has (...)
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  • A non-inversion theorem for the jump operator.Richard A. Shore - 1988 - Annals of Pure and Applied Logic 40 (3):277-303.
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  • Classes of Recursively Enumerable Sets and Degrees of Unsolvability.Donald A. Martin - 1966 - Mathematical Logic Quarterly 12 (1):295-310.
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  • Recursively enumerable generic sets.Wolfgang Maass - 1982 - Journal of Symbolic Logic 47 (4):809-823.
    We show that one can solve Post's Problem by constructing generic sets in the usual set theoretic framework applied to tiny universes. This method leads to a new class of recursively enumerable sets: r.e. generic sets. All r.e. generic sets are low and simple and therefore of Turing degree strictly between 0 and 0'. Further they supply the first example of a class of low recursively enumerable sets which are automorphic in the lattice E of recursively enumerable sets with inclusion. (...)
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  • Recursion, metarecursion, and inclusion.James C. Owings - 1967 - Journal of Symbolic Logic 32 (2):173-179.
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  • There is no fat orbit.Rod Downey & Leo Harrington - 1996 - Annals of Pure and Applied Logic 80 (3):277-289.
    We give a proof of a theorem of Harrington that there is no orbit of the lattice of recursively enumerable sets containing elements of each nonzero recursively enumerable degree. We also establish some degree theoretical extensions.
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  • Splitting theorems in recursion theory.Rod Downey & Michael Stob - 1993 - Annals of Pure and Applied Logic 65 (1):1-106.
    A splitting of an r.e. set A is a pair A1, A2 of disjoint r.e. sets such that A1 A2 = A. Theorems about splittings have played an important role in recursion theory. One of the main reasons for this is that a splitting of A is a decomposition of A in both the lattice, , of recursively enumerable sets and in the uppersemilattice, R, of recursively enumerable degrees . Thus splitting theor ems have been used to obtain results about (...)
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  • Jumps of Hemimaximal Sets.Rod Downey & Mike Stob - 1991 - Mathematical Logic Quarterly 37 (8):113-120.
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  • Jumps of Hemimaximal Sets.Rod Downey & Mike Stob - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (8):113-120.
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  • Minimal pairs and high recursively enumerable degrees.S. B. Cooper - 1974 - Journal of Symbolic Logic 39 (4):655-660.
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  • A jump class of noncappable degrees.S. B. Cooper - 1989 - Journal of Symbolic Logic 54 (2):324-353.
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  • The translation theorem.Peter Cholak - 1994 - Archive for Mathematical Logic 33 (2):87-108.
    We state and prove the Translation Theorem. Then we apply the Translation Theorem to Soare's Extension Theorem, weakening slightly the hypothesis to yield a theorem we call the Modified Extension Theorem. We use this theorem to reprove several of the known results about orbits in the lattice of recursively enumerable sets. It is hoped that these proofs are easier to understand than the old proofs.
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