Some remarks on the algebraic structure of the Medvedev lattice

Journal of Symbolic Logic 55 (2):831-853 (1990)
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Abstract

This paper investigates the algebraic structure of the Medvedev lattice M. We prove that M is not a Heyting algebra. We point out some relations between M and the Dyment lattice and the Mucnik lattice. Some properties of the degrees of enumerability are considered. We give also a result on embedding countable distributive lattices in the Medvedev lattice

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Citations of this work

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.
Intermediate logics and factors of the Medvedev lattice.Andrea Sorbi & Sebastiaan A. Terwijn - 2008 - Annals of Pure and Applied Logic 155 (2):69-85.
Characterizing the Join-Irreducible Medvedev Degrees.Paul Shafer - 2011 - Notre Dame Journal of Formal Logic 52 (1):21-38.
Constructive Logic and the Medvedev Lattice.Sebastiaan A. Terwijn - 2006 - Notre Dame Journal of Formal Logic 47 (1):73-82.

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References found in this work

Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.
Distributive Lattices.Raymond Balbes & Philip Dwinger - 1977 - Journal of Symbolic Logic 42 (4):587-588.

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