Inductive inference and unsolvability

Journal of Symbolic Logic 56 (3):891-900 (1991)
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.
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DOI 10.2178/jsl/1183743737
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Frank Stephan (1998). Learning Via Queries and Oracles. Annals of Pure and Applied Logic 94 (1-3):273-296.

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