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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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Journal ArticleDOI
Hierarchies of function classes defined by the first-value operator
TL;DR: The first-value operator is applied to establish hierarchies of classes of functions under various settings to obtain a hierarchy connected with Ershov's one within Δ 0 2 and Hausdorff's difference hierarchy in the Borel class.
Posted Content
Limit complexities revisited
TL;DR: The low-basis theorem can be used to get alternative proofs of the results on Kolmogorov complexity and to improve the result about effectively open sets and this stronger version implies the 2-randomness criterion.
Dissertation
Learning, realizability and games in classical arithmetic
TL;DR: There is a one-to-one correspondence between realizers and recursive winning strategies in the 1-Backtracking version of Tarski games and a new realizability semantics is introduced, called "Interactive Learning-Based Realizability".
Journal ArticleDOI
On the structures inside truth-table degrees
TL;DR: The following theorems on the structure inside nonrecursive truth-table degrees are established: Dëgtev's result that the number of bounded truth-Table degrees inside a truth- table degree is at least two is improved by showing that this number is infinite.
Book ChapterDOI
Automata, Circuits, and Hybrids: Facets of Continuous Time
TL;DR: Development is in particular evident in the area that covers the following three interrelated trends: automata, logic (arguing about automata) and interaction (composition of automata).