The automorphism group and definability of the jump operator in the ω-enumeration degrees

In the present paper, we show the first-order definability of the jump operator in the upper semi-lattice of the ω -enumeration degrees. As a consequence, we derive the isomorphicity of the automorphism groups of the enumeration and the ω -enumeration degrees.

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Bibliographic Details
Published in:Archive for mathematical logic 2021-11, Vol.60 (7-8), p.909-925
Main Authors: Ganchev, Hristo, Sariev, Andrey C.
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
Enumeration
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
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Description
Summary:In the present paper, we show the first-order definability of the jump operator in the upper semi-lattice of the ω -enumeration degrees. As a consequence, we derive the isomorphicity of the automorphism groups of the enumeration and the ω -enumeration degrees.
ISSN:0933-5846
1432-0665
DOI:10.1007/s00153-021-00766-7