Robust separations in inductive inference

Results in recursion-theoretic inductive inference have been criticized as depending on unrealistic self-referential examples. J.M. Barzdin (1974) proposed a way of ruling out such examples and conjectured that one of the earliest results of inductive inference theory would fall if his method were used. The author refutes Barzdin´s conjecture and proposes a new line of research examining robust separations which are defined using a strengthening of Barzdin´s original idea. Preliminary results are presented, and the most important open problem is stated as a conjecture. The extension of this work from function learning to formal language learning is discussed