Degree Spectra of Relations on a Cone

ISBN-13: 9781470428396 / Angielski

Matthew Harrison-Trainor

Opis

Let $mathcal A$ be a mathematical structure with an additional relation $R$. The author is interested in the degree spectrum of $R$, either among computable copies of $mathcal A$ when $(mathcal A,R)$ is a ``natural'' structure, or (to make this rigorous) among copies of $(mathcal A,R)$ computable in a large degree d. He introduces the partial order of degree spectra on a cone and begin the study of these objects. Using a result of Harizanov--that, assuming an effectiveness condition on $mathcal A$ and $R$, if $R$ is not intrinsically computable, then its degree spectrum contains all c.e. degrees--the author shows that there is a minimal non-trivial degree spectrum on a cone, consisting of the c.e. degrees.

Spis treści

• Introduction
• Preliminaries
• Degree spectra between the C.E. degrees and the D.C.E. degrees
• Degree spectra of relations on the naturals
• A ``fullness'' theorem for 2-CEA degrees
• Further questions
• Appendix A. relativizing Harizanov's theorem on C.E. degrees
• Bibliography
• Index of notation and terminology.