Mathematical Logic Quarterly 48 (S1):131-156 (2002)

Abstract
A real number is recursively approximable if there is a computable sequence of rational numbers converging to it. If some extra condition to the convergence is added, then the limit real number might have more effectivity. In this note we summarize some recent attempts to classify the recursively approximable real numbers by the convergence rates of the corresponding computable sequences ofr ational numbers
Keywords left and right computable reals  Weakly computable reals  random r.e. reals  divergence bounded computable reals  Recursively approximable reals  R.e. reals  Computable reals  semi‐computable reals
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DOI 10.1002/1521-3870(200210)48:1
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Approximation Representations for Δ2 Reals.George Barmpalias - 2004 - Archive for Mathematical Logic 43 (8):947-964.
Specker Sequences Revisited.Jakob G. Simonsen - 2005 - Mathematical Logic Quarterly 51 (5):532-540.

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