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  1. Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1987 - MIT Press.
  • Nowhere simple sets and the lattice of recursively enumerable sets.Richard A. Shore - 1978 - Journal of Symbolic Logic 43 (2):322-330.
  • Q 1-degrees of c.e. sets.R. Sh Omanadze & Irakli O. Chitaia - 2012 - Archive for Mathematical Logic 51 (5-6):503-515.
    We show that the Q-degree of a hyperhypersimple set includes an infinite collection of Q 1-degrees linearly ordered under ${\leq_{Q_1}}$ with order type of the integers and consisting entirely of hyperhypersimple sets. Also, we prove that the c.e. Q 1-degrees are not an upper semilattice. The main result of this paper is that the Q 1-degree of a hemimaximal set contains only one c.e. 1-degree. Analogous results are valid for ${\Pi_1^0}$ s 1-degrees.
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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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  • Some Properties of Recursively Inseparable Sets.J. P. Cleave - 1970 - Mathematical Logic Quarterly 16 (2):187-200.