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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.

Information

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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