Abstract of Paper

Ershov's Hierarchy of Real Numbers
by Xizhong Zheng, Robert Rettinger and Romain Gengler

Abstract:

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.