ABSTRACT
The relation between computation and definability by logical formulas is one of the cornerstones of computability theory, cf. Odifreddi [9], Rogers [14]. Interestingly, prior to his fundamental contribution to the theory of induction [3], Gold already wrote about limit computability [2], apparently unaware of earlier work of Shoenfield [15]. The book by Kelly [6] and the paper Gasarch et al. [1] contain topological characterizations of classes of functions that have a classifier, which is a method for deciding whether a function is in the given class or not. Although technically different, some of these results are similar in form to results such as Theorem 1.2 and Proposition 2.6 below. The role of limit computability in mathematics in general is investigated in the project by Hayashi [4].
