Constructive Logic and the Medvedev Lattice

Notre Dame Journal of Formal Logic 47 (1):73-82 (2006)
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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 degrees

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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.

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References found in this work

[Omnibus Review].M. Lerman - 1985 - Journal of Symbolic Logic 50 (2):550-552.
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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