As can be proved, uniform solvability of collections of solvable identification problems is rather influenced by the description of the problems than by the particular problems themselves. When prescribing a specific inference criterion (for example learning in the limit), a clever choice of descriptions allows uniform solvability of all solvable problems, whereas even the most simple classes of recursive functions are not uniformly learnable without restricting the set of possible descriptions. Furthermore the influence of the hypothesis spaces on uniform learnability is analysed.