Notre Dame Journal of Formal Logic

Constructive Logic and the Medvedev Lattice

Sebastiaan A. Terwijn


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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Notre Dame J. Formal Logic, Volume 47, Number 1 (2006), 73-82.

First available in Project Euclid: 27 March 2006

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Zentralblatt MATH identifier

Primary: 03D30: Other degrees and reducibilities 03B55: Intermediate logics 03G10: Lattices and related structures [See also 06Bxx]
Secondary: 03D80: Applications of computability and recursion theory

intuitionistic propositional logic Medvedev degrees Muchnik degrees computability


Terwijn, Sebastiaan A. Constructive Logic and the Medvedev Lattice. Notre Dame J. Formal Logic 47 (2006), no. 1, 73--82. doi:10.1305/ndjfl/1143468312.

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