d-computable categoricity for algebraic fields
Russell Miller
Source: J. Symbolic Logic Volume 74, Issue 4
(2009), 1325-1351.
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'=0'', 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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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1254748694
Digital Object Identifier: doi:10.2178/jsl/1254748694
Zentralblatt MATH identifier: 05654333
Mathematical Reviews number (MathSciNet): MR2583823
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