Abstract
An algebraic field extension of ℚ or ℤ/(p) may be regarded either as a structure in its own right, or as a subfield of its algebraic closure F (either ℚ or ℤ/(p)). We consider the Turing degree spectrum of F in both cases, as a structure and as a relation on F, and characterize the sets of Turing degrees that are realized as such spectra. The results show a connection between enumerability in the structure F and computability when F is seen as a subfield of F. © 2009 Springer Berlin Heidelberg.
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CITATION STYLE
Frolov, A., Kalimullin, I., & Miller, R. (2009). Spectra of algebraic fields and subfields. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5635 LNCS, pp. 232–241). https://doi.org/10.1007/978-3-642-03073-4_24
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