structural:expansion, structural:scholar_edition, quality:corruption
Numberings

A numbering is an enumeration of functions; it has two parameters, e and x and outputs the value of the e -th function in the numbering on the input x. Numberings can be partial-computable although some of its members are total computable functions. Admissible numberings are those into which all others can be translated. A Friedberg numbering (named after its discoverer) is a one-one numbering of all partial-computable functions; it is necessarily not an admissible numbering. Later research dealt also with numberings of other classes like classes of computably enumerable sets. Goncharov discovered for example a class of computably enumerable sets for which the numberings fall into exactly two classes with respect to computable isomorphisms.