The ∀∃-theory of the effectively closed Medvedev degrees is decidable

Archive for Mathematical Logic 49 (1):1-16 (2010)
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Abstract

We show that there is a computable procedure which, given an ∀∃-sentence ${\varphi}$ in the language of the partially ordered sets with a top element 1 and a bottom element 0, computes whether ${\varphi}$ is true in the Medvedev degrees of ${\Pi^0_1}$ classes in Cantor space, sometimes denoted by ${\mathcal{P}_s}$

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Citations of this work

A Survey of Mučnik and Medvedev Degrees.Peter G. Hinman - 2012 - Bulletin of Symbolic Logic 18 (2):161-229.
Inside the Muchnik Degrees I: Discontinuity, Learnability and Constructivism.K. Higuchi & T. Kihara - 2014 - Annals of Pure and Applied Logic 165 (5):1058-1114.
Coding True Arithmetic in the Medvedev Degrees of Classes.Paul Shafer - 2012 - Annals of Pure and Applied Logic 163 (3):321-337.

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References found in this work

Mass Problems and Randomness.Stephen G. Simpson - 2005 - Bulletin of Symbolic Logic 11 (1):1-27.
A Splitting Theorem for the Medvedev and Muchnik Lattices.Stephen Binns - 2003 - Mathematical Logic Quarterly 49 (4):327.
Working Below a Low2 Recursively Enumerably Degree.Richard A. Shore & Theodore A. Slaman - 1990 - Archive for Mathematical Logic 29 (3):201-211.
Density of the Medvedev Lattice of Π0 1 Classes.Douglas Cenzer & Peter G. Hinman - 2003 - Archive for Mathematical Logic 42 (6):583-600.

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