Complexity of index sets and translating functions

Abstract

The connection between index stes appearing in recursive enumerations of subrecursive classes and translating functions is investigated. Referring to a construction, which yields enumerations with low complexity for some index sets, we show that in such a case the complexity for some translating functions must be high. Furthermore a class of enumerations is discussed, which has elementary translating functions, but an important part of the index sets is not decidable by algorithms of the enumerated class (these index sets are of the form { $\mathit{x}:{\mathit{\psi }}_{\mathit{x}}\mathrm{(}\mathit{a}\mathrm{)}=\mathit{f}\mathrm{(}\mathit{x}\mathrm{)}$ }).