Notre Dame Journal of Formal Logic 49 (2):127-136 (2008)

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
Keywords mass problems   intuitionism   Brouwerian lattice   Heyting algebra   degrees of unsolvability
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DOI 10.1215/00294527-2008-002
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References found in this work BETA

An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Warszawa, Pwn - Polish Scientific Publishers.
Mass Problems and Randomness.Stephen G. Simpson - 2005 - Bulletin of Symbolic Logic 11 (1):1-27.
The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Journal of Symbolic Logic 9 (4):96-97.
A Splitting Theorem for the Medvedev and Muchnik Lattices.Stephen Binns - 2003 - Mathematical Logic Quarterly 49 (4):327.

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Citations of this work BETA

A Survey of Mučnik and Medvedev Degrees.Peter G. Hinman - 2012 - Bulletin of Symbolic Logic 18 (2):161-229.
Topological Aspects of the Medvedev Lattice.Andrew Em Lewis, Richard A. Shore & Andrea Sorbi - 2011 - Archive for Mathematical Logic 50 (3-4):319-340.
Mass Problems and Measure-Theoretic Regularity.Stephen G. Simpson - 2009 - Bulletin of Symbolic Logic 15 (4):385-409.
Effectively Closed Mass Problems and Intuitionism.Kojiro Higuchi - 2012 - Annals of Pure and Applied Logic 163 (6):693-697.

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