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About Degree Spectra of Relations on a Cone (Memoirs of the American Mathematical Society)
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.
Detailed Information
| Author: | Matthew Harrison-Trainor |
|---|---|
| Publication Year: | 2018 |
| ISBN: | 9781470428396 |
| Pages: | 120 |
| Language: | English |
| File Size: | 1.2 |
| Format: | |
| Price: | FREE |
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