Displaying similar documents to “Computable structures and operations on the space of continuous functions”

Computable categoricity versus relative computable categoricity

Rodney G. Downey, Asher M. Kach, Steffen Lempp, Daniel D. Turetsky (2013)

Fundamenta Mathematicae

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We study the notion of computable categoricity of computable structures, comparing it especially to the notion of relative computable categoricity and its relativizations. We show that every 1 decidable computably categorical structure is relatively Δ⁰₂ categorical. We study the complexity of various index sets associated with computable categoricity and relative computable categoricity. We also introduce and study a variation of relative computable categoricity, comparing it to both...

Computable analysis

Stanisław Mazur

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CONTENTS Foreword.......................................................................................... 3 I. Recursive and computable numbers...................................... 4 1. Recursive numbers................................................................... 5 2. Computable numbers............................................................... 17 II. Recursive and computable sequences................................. 22 III. Recursive and computable functionals....................................

On the hierarchies of Δ -real numbers

Xizhong Zheng (2007)

RAIRO - Theoretical Informatics and Applications

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A real number is called Δ if its binary expansion corresponds to a Δ -set of natural numbers. Such reals are just the limits of computable sequences of rational numbers and hence also called computably approximable. Depending on how fast the sequences converge, Δ -reals have different levels of effectiveness. This leads to various hierarchies of Δ reals. In this survey paper we summarize several recent developments related...