Results in recursion-theoretic inductive inference have been criticized as depending on unrealistic self-referential examples. J. M. Bārzdiņš 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. In this paper we refute Bārzdiņš' conjecture.
We propose a new line of research examining robust separations; these are defined using a strengthening of Bārzdiņš' original idea. The preliminary results of the new line of research are presented, and the most important open problem is stated as a conjecture. Finally, we discuss the extension of this work from function learning to formal language learning.