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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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Turing Incomparability in Scott Sets
TL;DR: For every Scott set F and every non-recursive set X in F, there is a Y in F such that X and Y are Turing incomparable as mentioned in this paper, where Y is a non-Turing incomparable set.
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Non-Turing computations via Malament-Hogarth space-times
Gabor Etesi,István Németi +1 more
TL;DR: In this paper, the authors investigate the Church-Kalm-Kreisel-Turing Theses concerning theoretical limitations of future computers and of deductive sciences, in view of recent results of classical general relativity theory.
Journal Article
Infinite limits and R-recursive functions
TL;DR: It is proved that the class of R-recursive functions is closed under this operation, which uses infinite limits to define R-Recursive functions.
Book ChapterDOI
The small grzegorczyk classes and the typed λ-calculus
Lars Kristiansen,Mathias Barra +1 more
TL;DR: The class of Grzegorczyk relations was introduced by Gandy and Paris-Wilkie as discussed by the authors, who considered the class of primitive relations and the small relational GrzEGorczyk classes.