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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
Reflecting in Epistemic Arithmetic
TL;DR: An epistemic formalization of arithmetic is constructed in which certain non-trivial metatheoretical inferences about the system itself can be made, but cannot be made in any consistent extensions of Stewart Shapiro's system of epistemic arithmetic.
Proceedings Article
Consistent Partial Identification.
Sanjay Jain,Frank Stephan +1 more
TL;DR: This study contrasts consistent partial identification with learning in the limit with the version of consistency where the learner has to be defined and consistent on all inputs and shows that the power of the learning criterion depends on whether the function to be learnt is fed in canonical order or in arbitrary order.
Book ChapterDOI
Algorithms and Decision Problems: A Crash Course in Recursion Theory
TL;DR: Questions about decidability boil down to questions about all algorithms, which explains the interest of the study of algorithms for logicians.
Book ChapterDOI
Chapter 3 Reducibilities
TL;DR: This chapter presents an overview of the most important arithmetical reducibilities and degrees other than Turing's, selected because of their intrinsic interest, testified not only by their natural definitions and connections with other areas but also by the quantity of results obtained from them.
Journal ArticleDOI
The approximation structure of a computably approximable real
TL;DR: An approach for a uniform classification of the computably approximable real numbers, consisting of the limits of computable sequences of rationals, and it coincides with the 0′-computable reals.