  In previous work, we have combined computable structure theory and
algorithmic learning theory to study which families of algebraic structures are
learnable in the limit (up to isomorphism). In this paper, we measure the
computational power that is needed to learn finite families of structures. In
particular, we prove that, if a family of structures is both finite and
learnable, then any oracle which computes the Halting set is able to achieve
such a learning. On the other hand, we construct a pair of structures which is
learnable but no computable learner can learn it.
