In language learning, strong relationships between Gold-style models and query models have recently been observed: in some quite general setting Gold-style learners can be replaced by query learners and vice versa, without loss of learning capabilities. These ‘equalities’ hold in the context of learning indexable classes of recursive languages. Former studies on Gold-style learning of such indexable classes have shown that, in many settings, the enumerability of the target class and the recursiveness of its languages are crucial for learnability. Moreover, studying query learning, non-indexable classes have been mainly neglected up to now. So it is conceivable that the recently observed relations between Gold-style and query learning are not due to common structures in the learning processes in both models, but rather to the enumerability of the target classes or the recursiveness of their languages. In this paper, the analysis is lifted onto the context of learning arbitrary class...