Numbering (computability theory)

In computability theory a numbering is the assignment of natural numbers to a set of objects like rational numbers, graphs or words in some language. A numbering can be used to transfer the computability concept, which is strictly defined on the natural numbers using computable functions, to different objects.

Important numerations are the Gödel numbering of the terms in first-order predicate calculus and numerations of the set of computable functions which can be used to apply results of computability theory on the set of computable functions itself.