On the hierarchies of Δ -real numbers
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...