The approximation structure of a computably approximable real

Journal of Symbolic Logic 68 (3):885-922 (2003)
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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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Citations of this work

Hypersimplicity and semicomputability in the weak truth table degrees.George Barmpalias - 2005 - Archive for Mathematical Logic 44 (8):1045-1065.
Approximation Representations for Δ2 Reals.George Barmpalias - 2004 - Archive for Mathematical Logic 43 (8):947-964.
Approximation representations for reals and their wtt‐degrees.George Barmpalias - 2004 - Mathematical Logic Quarterly 50 (4-5):370-380.

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References found in this work

Classical Recursion Theory.Peter G. Hinman - 2001 - Bulletin of Symbolic Logic 7 (1):71-73.
Recursive Approximability of Real Numbers.Xizhong Zheng - 2002 - Mathematical Logic Quarterly 48 (S1):131-156.

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