## Journal of Symbolic Logic

### Inductive Inference and Unsolvability

#### Abstract

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 $f(0), f(1), f(2),\ldots$. 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 $f(0), f(1), f(2),\ldots$ has value unequal to zero for infinitely many arguments. Finally, it is shown that these unsolvable problems are strictly easier than the halting problem.

#### Article information

Source
J. Symbolic Logic Volume 56, Issue 3 (1991), 891-900.

Dates
First available in Project Euclid: 6 July 2007

http://projecteuclid.org/euclid.jsl/1183743737

JSTOR