d-computable Categoricity for Algebraic Fields

Journal of Symbolic Logic 74 (4):1325 - 1351 (2009)
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Abstract

We use the Low Basis Theorem of Jockusch and Soare to show that all computable algebraic fields are d-computably categorical for a particular Turing degree d with d' = θ", but that not all such fields are 0'-computably categorical. We also prove related results about algebraic fields with splitting algorithms, and fields of finite transcendence degree over ℚ

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Citations of this work

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Categoricity Spectra for Polymodal Algebras.Nikolay Bazhenov - 2016 - Studia Logica 104 (6):1083-1097.
Effective algebraicity.Rebecca M. Steiner - 2013 - Archive for Mathematical Logic 52 (1-2):91-112.

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References found in this work

Generic copies of countable structures.Chris Ash, Julia Knight, Mark Manasse & Theodore Slaman - 1989 - Annals of Pure and Applied Logic 42 (3):195-205.
Theorie Der Numerierungen III.Ju L. Erš - 1977 - Mathematical Logic Quarterly 23 (19-24):289-371.
Theorie Der Numerierungen III.Ju L. Erš - 1976 - Mathematical Logic Quarterly 23 (19‐24):289-371.

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