Notre Dame Journal of Formal Logic

Constructive Logic and the Medvedev Lattice

Sebastiaan A. Terwijn

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.

Article information

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

Dates
First available in Project Euclid: 27 March 2006

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1143468312

Digital Object Identifier
doi:10.1305/ndjfl/1143468312

Mathematical Reviews number (MathSciNet)
MR2211183

Zentralblatt MATH identifier
1107.03024

Subjects
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

Keywords
intuitionistic propositional logic Medvedev degrees Muchnik degrees computability

Citation

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. http://projecteuclid.org/euclid.ndjfl/1143468312.


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References

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