Inductive Inference of Recursive Functions: Qualitative Theory

This survey contains both old and very recent results in non-quantitative aspects of inductive inference of total recursive functions. The survey is not complete. The paper was written to stress some of the main results in selected directions of research performed at the University of Latvia rather than to exhaust all of the obtained results. We concentrated on the more explored areas such as the inference of indices in non-Goedel computable numberings, the inference of minimal Goedel numbers, and the specifics of inference of minimal indices in Kolmogorov numberings.