The complexity of universal text-learners

The present work deals with language learning from text. It considers universal learners for classes of languages in models of additional information and analyzes their complexity in terms of Turing-degrees. The following is shown: If the additional information is given by a set containing at least one index for each language from the class to be learned but no index for any language outside the class then there is a universal learner having the same Turing degree as the inclusion problem for enumerable sets. This result is optimal in the sense that any further learner has the same or higher Turing degree. If the additional information is given by a set which contains exactly the indices of the languages from the class to be learned then there is a computable universal learner. Finally, if the additional information is presented as an upper bound on the size of some grammar that generates the language then a high oracle is necessary and sufficient.