Abstract
A natural ω pLω+1 hierarchy of successively more general criteria of success for inductive inference machines is described based on the size of sets of anomalies in programs synthesized by such machines. These criteria are compared to others in the literature. Some of our results are interpreted as tradeoff results or as showing the inherent relative-computational complexity of certain processes and others are interpreted from a positivistic, mechanistic philosophical stance as theorems in philosophy of science. The techniques of recursive function theory are employed including ordinary and infinitary recursion theorems.
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