Enumeration Problem

An algorithmic problem in which one has to construct an algorithm that enumerates $ A $ for a given set $ A $, i.e. an algorithm $ \mathfrak A $ that is applicable to any natural number, that converts it to an element of $ A $ and such that any element of $ A $ is obtained by applying $ \mathfrak A $ to some natural number; in other words, $ A = \{ {\mathfrak A ( i) } : {i \in \mathbf N } \} $. The enumeration problem for a set $ A $ is solvable (i.e. such an $ \mathfrak A $ exists) if and only if $ A $ is a non-empty enumerable set.