Notre Dame Journal of Formal Logic

Mass Problems and Intuitionism

Stephen G. Simpson

Abstract

Let $\mathcal{P}_w$ be the lattice of Muchnik degrees of nonempty $\Pi^0_1$ subsets of $2^\omega$. The lattice $\mathcal{P}$ has been studied extensively in previous publications. In this note we prove that the lattice $\mathcal{P}$ is not Brouwerian.

Article information

Source
Notre Dame J. Formal Logic Volume 49, Number 2 (2008), 127-136.

Dates
First available in Project Euclid: 15 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1210859922

Digital Object Identifier
doi:10.1215/00294527-2008-002

Mathematical Reviews number (MathSciNet)
MR2402036

Zentralblatt MATH identifier
1141.03018

Subjects
Primary: 03D30: Other degrees and reducibilities
Secondary: 03D28: Other Turing degree structures 03D80: Applications of computability and recursion theory 03B20: Subsystems of classical logic (including intuitionistic logic) 03F55: Intuitionistic mathematics 06D20: Heyting algebras [See also 03G25]

Keywords
mass problems intuitionism Brouwerian lattice Heyting algebra degrees of unsolvability

Citation

Simpson, Stephen G. Mass Problems and Intuitionism. Notre Dame J. Formal Logic 49 (2008), no. 2, 127--136. doi:10.1215/00294527-2008-002. https://projecteuclid.org/euclid.ndjfl/1210859922


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