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d-computable Categoricity for Algebraic Fields

Russell Miller
The Journal of Symbolic Logic
Vol. 74, No. 4 (Dec., 2009), pp. 1325-1351
Stable URL: http://www.jstor.org/stable/40378270
Page Count: 27
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
d-computable Categoricity for Algebraic Fields
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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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