Archive for Mathematical Logic 43 (3):399-414 (2004)

Abstract
Let w and M be the countable distributive lattices of Muchnik and Medvedev degrees of non-empty Π1 0 subsets of 2ω, under Muchnik and Medvedev reducibility, respectively. We show that all countable distributive lattices are lattice-embeddable below any non-zero element of w . We show that many countable distributive lattices are lattice-embeddable below any non-zero element of M
Keywords Mathematics
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DOI 10.1007/s00153-003-0195-x
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References found in this work BETA

A Splitting Theorem for the Medvedev and Muchnik Lattices.Stephen Binns - 2003 - Mathematical Logic Quarterly 49 (4):327.
Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.

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Citations of this work BETA

Mass Problems and Randomness.Stephen G. Simpson - 2005 - Bulletin of Symbolic Logic 11 (1):1-27.
Mass Problems and Hyperarithmeticity.Joshua A. Cole & Stephen G. Simpson - 2007 - Journal of Mathematical Logic 7 (2):125-143.
A Survey of Mučnik and Medvedev Degrees.Peter G. Hinman - 2012 - Bulletin of Symbolic Logic 18 (2):161-229.
The Medvedev Lattice of Computably Closed Sets.Sebastiaan A. Terwijn - 2006 - Archive for Mathematical Logic 45 (2):179-190.
Mass Problems and Measure-Theoretic Regularity.Stephen G. Simpson - 2009 - Bulletin of Symbolic Logic 15 (4):385-409.

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