A note on the enumeration degrees of 1-generic sets

We show that every nonzero Δ 2 0 enumeration degree bounds the enumeration degree of a 1-generic set. We also point out that the enumeration degrees of 1-generic sets, below the first jump, are not downwards closed, thus answering a question of Cooper.

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Bibliographic Details
Published in:Archive for mathematical logic 2016-05, Vol.55 (3-4), p.405-414
Main Authors: Badillo, Liliana, Bianchini, Caterina, Ganchev, Hristo, Kent, Thomas F., Sorbi, Andrea
Format: Article
Language:English
Subjects:
Algebra
Archives
Enumeration
Formulas (mathematics)
Mathematical logic
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
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Summary:We show that every nonzero Δ 2 0 enumeration degree bounds the enumeration degree of a 1-generic set. We also point out that the enumeration degrees of 1-generic sets, below the first jump, are not downwards closed, thus answering a question of Cooper.
ISSN:0933-5846
1432-0665
DOI:10.1007/s00153-015-0471-6