Let X be a unary relation on the domain of (ω,<). The degree spectrum of X on (ω,<) is the set of Turing degrees of the image of X in all computable presentations of (ω,<). Many results are known about the types of degree spectra that are possible for relations forming infinite and coinfinite c.e. sets, high c.e. sets and non-high c.e. sets on the standard copy. We show that if the degree spectrum of X contains the computable degree then its degree spectrum is precisely the set of Δ_2 degrees.
The structure ζ can be viewed as a copy of ω* followed by a copy of ω and, for this reason, the degree spectrum of X on ζ can be largely understood from the work on ω. A helpful correspondence between the degree spectra on ω and ζ is presented and the known results for degree spectra on the former structure are extended to analogous results for the latter.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/4544 |
| Date | January 2009 |
| Creators | Knoll, Carolyn Alexis |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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