dc.contributor.author | Knoll, Carolyn Alexis | |
dc.date.accessioned | 2009-08-13 18:45:13 (GMT) | |
dc.date.available | 2009-08-13 18:45:13 (GMT) | |
dc.date.issued | 2009-08-13T18:45:13Z | |
dc.date.submitted | 2009 | |
dc.identifier.uri | http://hdl.handle.net/10012/4544 | |
dc.description.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. | en |
dc.language.iso | en | en |
dc.publisher | University of Waterloo | en |
dc.subject | Logic | en |
dc.subject | Computable Structure Theory | en |
dc.subject | Degree Spectrum | en |
dc.subject | Linear Orders | en |
dc.title | Degree Spectra of Unary relations on ω and ζ | en |
dc.type | Master Thesis | en |
dc.pending | false | en |
dc.subject.program | Pure Mathematics | en |
uws-etd.degree.department | Pure Mathematics | en |
uws-etd.degree | Master of Mathematics | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Unreviewed | en |
uws.scholarLevel | Graduate | en |