On relative enumerability of Turing degrees
β Scribed by Shamil Ishmukhametov
- Publisher
- Springer
- Year
- 2000
- Tongue
- English
- Weight
- 89 KB
- Volume
- 39
- Category
- Article
- ISSN
- 0933-5846
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## Abstract This paper continues our study of computable pointβfree topological spaces and the metamathematical points in them. For us, a __point__ is the intersection of a sequence of basic open sets with compact and nested closures. We call such a sequence a __sharp filter__. A function __f~F~__
Let A be an inΓΏnite computable structure, and let R be an additional computable relation on its domain A. The syntactic notion of formal hypersimplicity of R on A, ΓΏrst introduced and studied by Hird, is analogous to the computability-theoretic notion of hypersimplicity of R on A, given the deΓΏnabil
A model is computable if its domain is a computable set and its relations and functions are uniformly computable. Let ~2 be a computable model and let R be an extra relation on the domain of &. That is, R is not named in the language of .d. We define Dgd(R) to be the set of Turing degrees of the ima