Inductive inference and unsolvability

It is shown that many different problems have the same degree of unsolvability. Among these problems are: The Inductive Inference Problem. Infer in the limit an index for a recursive function f presented as f (0), f (1), f (2),…. The Recursive Index Problem. Decide in the limit if i is the index of a total recursive function . The Zero Nonvariant Problem. Decide in the limit if a recursive function f presented as f (0), f (1), f (2),… has value unequal to zero for infinitely many arguments . Finally, it is shown that these unsolvable problems are strictly easier than the halting problem.