Some remarks on the algebraic structure of the Medvedev lattice

Journal of Symbolic Logic 55 (2):831-853 (1990)
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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DOI 10.2307/2274668
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Intermediate Logics and Factors of the Medvedev Lattice.Andrea Sorbi & Sebastiaan A. Terwijn - 2008 - Annals of Pure and Applied Logic 155 (2):69-85.
Effectively Closed Mass Problems and Intuitionism.Kojiro Higuchi - 2012 - Annals of Pure and Applied Logic 163 (6):693-697.
Basic Subtoposes of the Effective Topos.Sori Lee & Jaap Van Oosten - 2013 - Annals of Pure and Applied Logic 164 (9):866-883.
Inside the Muchnik Degrees I: Discontinuity, Learnability and Constructivism.K. Higuchi & T. Kihara - 2014 - Annals of Pure and Applied Logic 165 (5):1058-1114.

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