Kripke Models, Distributive Lattices, and Medvedev Degrees

Studia Logica 85 (3):319-332 (2007)
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Abstract

We define a variant of the standard Kripke semantics for intuitionistic logic, motivated by the connection between constructive logic and the Medvedev lattice. We show that while the new semantics is still complete, it gives a simple and direct correspondence between Kripke models and algebraic structures such as factors of the Medvedev lattice.

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10.1007/s11225-007-9054-9

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Citations of this work

Mass Problems and Intuitionism.Stephen G. Simpson - 2008 - Notre Dame Journal of Formal Logic 49 (2):127-136.

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References found in this work

Semantical Analysis of Intuitionistic Logic I.Saul A. Kripke - 1963 - In Michael Dummett & J. N. Crossley (eds.), Formal Systems and Recursive Functions. Amsterdam,: North Holland. pp. 92-130.
On the interpretation of intuitionistic number theory.Stephen Cole Kleene - 1945 - Journal of Symbolic Logic 10 (4):109-124.
On the Interpretation of Intuitionistic Number Theory.S. C. Kleene - 1947 - Journal of Symbolic Logic 12 (3):91-93.
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.

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