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September 2003 The approximation structure of a computably approximable real
George Barmpalias
J. Symbolic Logic 68(3): 885-922 (September 2003). DOI: 10.2178/jsl/1058448447

Abstract

A new approach for a uniform classification of the computably approximable real numbers is introduced. This is an important class of reals, consisting of the limits of computable sequences of rationals, and it coincides with the 0’-computable reals. Unlike some of the existing approaches, this applies uniformly to all reals in this class: to each computably approximable real x we assign a degree structure, the structure of all possible ways available to approximate x. So the main criterion for such classification is the variety of the effective ways we have to approximate a real number. We exhibit extreme cases of such approximation structures and prove a number of related results.

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George Barmpalias. "The approximation structure of a computably approximable real." J. Symbolic Logic 68 (3) 885 - 922, September 2003. https://doi.org/10.2178/jsl/1058448447

Information

Published: September 2003
First available in Project Euclid: 17 July 2003

zbMATH: 1056.03040
MathSciNet: MR2004D:03132
Digital Object Identifier: 10.2178/jsl/1058448447

Subjects:
Primary: 03F60
Secondary: 03D30

Keywords: approximation structure , Computably approximable reals , immunity properties

Rights: Copyright © 2003 Association for Symbolic Logic

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Vol.68 • No. 3 • September 2003
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