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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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Non-computability of the equational theory of polyadic algebras
TL;DR: In this article, it was shown that the equational theory of RPA! is non-recursively enumerable in the generalized sense. But this result does not imply that RPA!, as a class of representable polyadic algebras, is also non-computable.
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Convergence of random series and the rate of convergence of the strong law of large numbers in game-theoretic probability
Kenshi Miyabe,Akimichi Takemura +1 more
TL;DR: A unified treatment of the convergence of random series and the rate of convergence of the strong law of large numbers in the framework of game-theoretic probability of Shafer and Vovk (2001) and some fundamental results on deterministic strategies of Reality are derived.
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Degrees of Infinite Words, Polynomials and Atoms
TL;DR: Methods from linear algebra and analysis are used to show that there is an infinite number of atoms in the transducer degrees, that is, minimal non-trivial degrees.
Journal ArticleDOI
The Implicit Computational Complexity of Imperative Programming Languages
TL;DR: This work extends and modify the theory of implicit computational complexity to work in a context of imperative programming languages, and characterise complexity classes like P, LINSPACE, PSPACE and the classes in the Grzegorczyk hiearchy.
Journal ArticleDOI
Subrecursive degrees and fragments of Peano Arithmetic
TL;DR: An isomorphic subrecursive degree structure <≤,?