Spectra of Algebraic Fields and Subfields

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. Key words: Computability, computable model theory, field, algebraic, spectrum.

• Type: Conference
• Year: 2009
• Where: CIE
• Authors: Andrey Frolov, Iskander Sh. Kalimullin, Russell Miller
• Keywords: Algebraic Field Extension, Applied Computing, CIE 2009, Turing Degree Spectrum, Turing Degrees