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d-computable categoricity for algebraic fields

Published online by Cambridge University Press:  12 March 2014

Russell Miller
Russell Miller*
Affiliation:
Department of Mathematics, Queens College – C.U.N.Y., 65-30 Kissena Blvd., Flushing, New York 11367, USA Ph.D. Programs in Computer Science & Mathematics, The Graduate Center of C.U.N.Y., 365 Fifth Avenue, New York, New York 10016, USA, E-mail: Russell.Miller@qc.cuny.edu
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 4 , December 2009 , pp. 1325 - 1351
Copyright
Copyright © Association for Symbolic Logic 2009

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