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Classical recursion theory
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Theories of Recursive functions, Hierarchies of recursive functions, and Arithmetical sets: Recursively enumerable sets.Abstract:
Preface. Introduction. Theories of Recursive functions. Hierarchies of recursive functions. Recursively enumerable sets. Recursively enumerable degrees. Limit sets. Arithmetical sets. Arithmetical degrees. Enumeration degrees. Bibliography. Notation index. Subject index.read more
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Strong Reductions and Immunity for Exponential Time
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A New Approach to Abstract Machines - Introduction to the Theory of Configuration Machines
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Highness, locally noncappability and nonboundings
Frank Stephan,Guohua Wu +1 more
TL;DR: It is proved that above any nonzero, incomplete recursively enumerable (r.e.) degree a, there is a high 2 r.e. degree c > a witnessing that a is locally noncappable (Theorem 1.1).
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Members of thin $\Pi ^0_1$ classes and generic degrees
TL;DR: In this paper, it was shown that all 2-generic degrees contain no members of thin classes, and that all 1-generic degree below Ω(n 0)$'$ contain members of these classes.