Journal of Symbolic Logic

d-computable categoricity for algebraic fields

Russell Miller

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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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J. Symbolic Logic, Volume 74, Issue 4 (2009), 1325-1351.

First available in Project Euclid: 5 October 2009

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Miller, Russell. d -computable categoricity for algebraic fields. J. Symbolic Logic 74 (2009), no. 4, 1325--1351. doi:10.2178/jsl/1254748694.

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