Mass problems and density

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Journal of Mathematical Logic 16 (2):1650006 (2016)
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Abstract

Recall that [Formula: see text] is the lattice of Muchnik degrees of nonempty effectively compact sets in Euclidean space. We solve a long-standing open problem by proving that [Formula: see text] is dense, i.e. satisfies [Formula: see text]. Our proof combines an oracle construction with hyperarithmetical theory.

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10.1142/s0219061316500069

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References found in this work

A splitting theorem for the Medvedev and Muchnik lattices.Stephen Binns - 2003 - Mathematical Logic Quarterly 49 (4):327.
Mass problems and hyperarithmeticity.Joshua A. Cole & Stephen G. Simpson - 2007 - Journal of Mathematical Logic 7 (2):125-143.
Density of the Medvedev lattice of Π0 1 classes.Douglas Cenzer & Peter G. Hinman - 2003 - Archive for Mathematical Logic 42 (6):583-600.
Density of the Medvedev lattice of Π01 classes.Douglas Cenzer & Peter G. Hinman - 2003 - Archive for Mathematical Logic 42 (6):583-600.
Coding true arithmetic in the Medvedev and Muchnik degrees.Paul Shafer - 2011 - Journal of Symbolic Logic 76 (1):267 - 288.

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