Editing Computability theory (section)

===Inductive inference===
This is the computability-theoretic branch of learning theory. It is based on [[E. Mark Gold]]'s model of learning in the limit from 1967 and has developed since then more and more models of learning. The general scenario is the following: Given a class ''S'' of computable functions, is there a learner (that is, computable functional) which outputs for any input of the form (''f''(0),&nbsp;''f''(1),&nbsp;...,&nbsp;''f''(''n'')) a hypothesis. A learner ''M'' learns a function ''f'' if almost all hypotheses are the same index ''e'' of ''f'' with respect to a previously agreed on acceptable numbering of all computable functions; ''M'' learns ''S'' if ''M'' learns every ''f'' in ''S''. Basic results are that all computably enumerable classes of functions are learnable while the class REC of all computable functions is not learnable. Many related models have been considered and also the learning of classes of computably enumerable sets from positive data is a topic studied from Gold's pioneering paper in 1967 onwards.