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On the hierarchies of Δ2 0-real numbers

Published online by Cambridge University Press:  24 April 2007

Xizhong Zheng
Xizhong Zheng*
Affiliation:
Department of Computer Science, Jiangsu University, Zhenjiang 212013, China. Theoretische Informatik, BTU Cottbus, 03044 Cottbus, Germany; zheng@tu-cottbus.de
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Abstract

A real number x is called Δ2 0 if its binary expansion corresponds to a Δ2 0-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, Δ2 0-reals have different levels of effectiveness. This leads to various hierarchies of Δ2 0 reals. In this survey paper we summarize several recent developments related to such kind of hierarchies shown by the author and his collaborators.

Keywords

Computably approximable realsΔ2 0-realshierarchy.

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Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 41 , Issue 1: Real Numbers , January 2007 , pp. 3 - 25
Copyright
© EDP Sciences, 2007

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