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Degree Spectra of Unary relations on ω and ζ

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.

Identiferoai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OWTU.10012/4544
Date January 2009
CreatorsKnoll, Carolyn Alexis
Source SetsLibrary and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation

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