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  1. Interpreting true arithmetic in the theory of the r.e. truth table degrees.André Nies & Richard A. Shore - 1995 - Annals of Pure and Applied Logic 75 (3):269-311.
    We show that the elementary theory of the recursively enumerable tt-degrees has the same computational complexity as true first-order arithmetic. As auxiliary results, we prove theorems about exact pairs and initial segments in the tt-degrees.
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  • Undecidability and initial segments of the (r.E.) TT-Degrees.Christine Ann Haught & Richard A. Shore - 1990 - Journal of Symbolic Logic 55 (3):987-1006.
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  • The d.r.e. degrees are not dense.S. Cooper, Leo Harrington, Alistair Lachlan, Steffen Lempp & Robert Soare - 1991 - Annals of Pure and Applied Logic 55 (2):125-151.
    By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees.
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  • The d.r.e. degrees are not dense.S. Barry Cooper, Leo Harrington, Alistair H. Lachlan, Steffen Lempp & Robert I. Soare - 1991 - Annals of Pure and Applied Logic 55 (2):125-151.
    By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees.
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