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  1.  50
    Topological aspects of the Medvedev lattice.Andrew Em Lewis, Richard A. Shore & Andrea Sorbi - 2011 - Archive for Mathematical Logic 50 (3-4):319-340.
    We study the Medvedev degrees of mass problems with distinguished topological properties, such as denseness, closedness, or discreteness. We investigate the sublattices generated by these degrees; the prime ideal generated by the dense degrees and its complement, a prime filter; the filter generated by the nonzero closed degrees and the filter generated by the nonzero discrete degrees. We give a complete picture of the relationships of inclusion holding between these sublattices, these filters, and this ideal. We show that the sublattice (...)
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  2.  35
    Randomness and the linear degrees of computability.Andrew Em Lewis & George Barmpalias - 2007 - Annals of Pure and Applied Logic 145 (3):252-257.
    We show that there exists a real α such that, for all reals β, if α is linear reducible to β then β≤Tα. In fact, every random real satisfies this quasi-maximality property. As a corollary we may conclude that there exists no ℓ-complete Δ2 real. Upon realizing that quasi-maximality does not characterize the random reals–there exist reals which are not random but which are of quasi-maximal ℓ-degree–it is then natural to ask whether maximality could provide such a characterization. Such hopes, (...)
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  3.  55
    Empty intervals in the enumeration degrees.Thomas F. Kent, Andrew Em Lewis & Andrea Sorbi - 2012 - Annals of Pure and Applied Logic 163 (5):567-574.