Degree spectra of relations on a cone
Author(s)
Bibliographic Information
Degree spectra of relations on a cone
（Memoirs of the American Mathematical Society, no. 1208）
American Mathematical Society, c2018
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Note
Includes bibliographical references and index
May 2018, volume 253, number 1208 (third of 7 numbers)
Description and Table of Contents
Description
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.
Table of Contents
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.
by "Nielsen BookData"
