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Topological aspects of the Medvedev lattice

Lewis-Pye, Andrew, Shore, Richard A. and Sorbi, Andrea (2011) Topological aspects of the Medvedev lattice. Archive for Mathematical Logic, 50 (3-4). pp. 319-340. ISSN 0933-5846

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Identification Number: 10.1007/s00153-010-0215-6


We study the Medvedev degrees of mass problems with distinguished topological properties, such as denseness, closedness, or discreteness. We investigate the sublattices generated by these degrees; the prime ideal generated by the dense degrees and its complement, a prime filter; the filter generated by the nonzero closed degrees and the filter generated by the nonzero discrete degrees. We give a complete picture of the relationships of inclusion holding between these sublattices, these filters, and this ideal. We show that the sublattice of the closed Medvedev degrees is not a Brouwer algebra. We investigate the dense degrees of mass problems that are closed under Turing equivalence, and we prove that the dense degrees form an automorphism base for the Medvedev lattice. The results hold for both the Medvedev lattice on the Baire space and the Medvedev lattice on the Cantor space.

Item Type: Article
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Additional Information: © 2011 Springer
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 06 Aug 2013 11:48
Last Modified: 20 Oct 2021 01:54

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