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| Title: | Degree Spectra of Unary relations on ω and ζ |
| Authors: | Knoll, Carolyn Alexis |
| Keywords: | Logic
Computable Structure Theory
Degree Spectrum
Linear Orders |
| Approved Date: | 13-Aug-2009 |
| Date Submitted: | 2009 |
| Abstract: | 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. |
| Program: | Pure Mathematics |
| Department: | Pure Mathematics |
| Degree: | Master of Mathematics |
| URI: | http://hdl.handle.net/10012/4544 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
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