Mathematical Logic Quarterly 48 (S1):157-181 (2002)

Abstract
For the computability of subsets of real numbers, several reasonable notions have been suggested in the literature. We compare these notions in a systematic way by relating them to pairs of ‘basic’ ones. They turn out to coincide for full-dimensional convex sets; but on the more general class of regular sets, they reveal rather interesting ‘weaker/stronger’ relations. This is in contrast to single real numbers and vectors where all ‘reasonable’ notions coincide
Keywords Regular Sets  Recursive Analysis  Computability
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DOI 10.1002/1521-3870(200210)48:1
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On Computable Numbers, with an Application to the N Tscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
Nicht Konstruktiv Beweisbare Sätze der Analysis.Ernst Specker - 1949 - Journal of Symbolic Logic 14 (3):145-158.

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