Learning Theory and Descriptive Set Theory
Kevin T. Kelly · Journal of Logic and Computation · 1993
This paper presents a generalized paradigm for formal learning theory, of which language leamability and recursive function identification are special cases. This perspective leads to general characterizations of discovery and hypothesis assessment, both for ideal and for computable scientists. The characterizations are in terms of Borel complexity in the ideal case and arithmetical complexity in the computational case. The perspective provides an epistemological interpretation of other areas of recursion theory, such as the recursion-theoretic basis theorems.