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Constructive Logic and the Medvedev Lattice
Notre Dame Journal of Formal Logic 47 (1):73-82 (2006)
Abstract
We study the connection between factors of the Medvedev lattice and constructive logic. The algebraic properties of these factors determine logics lying in between intuitionistic propositional logic and the logic of the weak law of the excluded middle (also known as De Morgan, or Jankov, logic). We discuss the relation between the weak law of the excluded middle and the algebraic notion of join-reducibility. Finally we discuss autoreducible degreesOther Versions
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Citations of this work
The Medvedev lattice of computably closed sets.Sebastiaan A. Terwijn - 2006 - Archive for Mathematical Logic 45 (2):179-190.
Characterizing the Join-Irreducible Medvedev Degrees.Paul Shafer - 2011 - Notre Dame Journal of Formal Logic 52 (1):21-38.
Mass Problems and Intuitionism.Stephen G. Simpson - 2008 - Notre Dame Journal of Formal Logic 49 (2):127-136.
Basic subtoposes of the effective topos.Sori Lee & Jaap van Oosten - 2013 - Annals of Pure and Applied Logic 164 (9):866-883.
Kripke Models, Distributive Lattices, and Medvedev Degrees.Sebastiaan A. Terwijn - 2007 - Studia Logica 85 (3):319-332.
References found in this work
Theory of recursive functions and effective computability.Hartley Rogers - 1987 - Cambridge: MIT Press.
Some remarks on the algebraic structure of the Medvedev lattice.Andrea Sorbi - 1990 - Journal of Symbolic Logic 55 (2):831-853.
Embedding Brouwer algebras in the Medvedev lattice.Andrea Sorbi - 1991 - Notre Dame Journal of Formal Logic 32 (2):266-275.
The Medvedev lattice of computably closed sets.Sebastiaan A. Terwijn - 2006 - Archive for Mathematical Logic 45 (2):179-190.
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