A Thesis in Inductive Inference

Inductive inference is the theory of identifying recursive functions from examples. In [26], [27], [30] the following thesis was stated: Any class of recursive functions which is identifiable at all can always be identified by an enumeratively working strategy. Moreover, the identification can always be realized with respect to a suitable nonstandard (i.e. non-Godel) numbering. We review some of the results which have led us to state this thesis. New results are presented concerning monotonic identification and corroborating the thesis. Some of the consequences of the thesis are discussed involving the development of the theory of inductive inference during the last decade. Problems of further investigation as well as further applications of non-Godel numberings in inductive inference are summarized.

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