Journal of Symbolic Logic

d-computable categoricity for algebraic fields

Russell Miller

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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'=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.

Article information

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

Dates
First available in Project Euclid: 5 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1254748694

Digital Object Identifier
doi:10.2178/jsl/1254748694

Mathematical Reviews number (MathSciNet)
MR2583823

Zentralblatt MATH identifier
1202.03044

Citation

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


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