|Abstract of Paper|
Ershov's Hierarchy of Real Numbers
by Xizhong Zheng, Robert Rettinger and Romain Gengler
Analogous to Ershov's hierarchy for $\Delta^0_2$-subsets of natural numbers we discuss the similar hierarchy for recursively approximable real numbers. Namely, we define the $k$-computability for natural number $k$ and $f$-computability for function $f$ based on different representations of real numbers. We will show that they are not equivalent for the representations based on Cauchy sequence, Dedekind cut and binary expansion.