Degree Spectra of Relations on a Cone

Matthew Harrison-Trainor (Autor)

Buch | Softcover

107 Seiten

2018
American Mathematical Society (Verlag)
978-1-4704-2839-6 (ISBN)

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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.

Matthew Harrison-Trainor, University of California, Berkeley, California.

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.

Erscheinungsdatum	22.08.2018
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	187 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
ISBN-10	1-4704-2839-3 / 1470428393
ISBN-13	978-1-4704-2839-6 / 9781470428396
Zustand	Neuware