Mass problems and density-Reference-Cited by-同舟云学术

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Mass problems and density

Published:2016-12 Issue:02 Volume:16 Page:1650006
ISSN:0219-0613
Container-title:Journal of Mathematical Logic
language:en
Short-container-title:J. Math. Log.

Author:

Binns Stephen¹,Shore Richard A.²,Simpson Stephen G.³

Affiliation:

1. Department of Mathematics, Statistics, and Physics, College of Arts and Sciences, Qatar University, P.O. Box 2713, Doha, Qatar

2. Department of Mathematics, Cornell University, Ithaca, NY 14853, USA

3. Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Logic

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219061316500069

Reference23 articles.

1. On the existence of a strong minimal pair

2. A splitting theorem for the Medvedev and Muchnik lattices

3. Density of the Medvedev lattice of ?01 classes

4. MASS PROBLEMS AND HYPERARITHMETICITY

5. The Upper Semi-Lattice of Degrees of Recursive Unsolvability

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