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A real number is called Δ
if its binary expansion corresponds to a Δ
-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, Δ
-reals have different levels of effectiveness. This leads to various hierarchies of Δ
reals. In this survey paper we summarize several recent developments related to such kind...
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