In computability theory a numbering is the assignment of natural numbers to a set of objects such as functions, rational numbers, graphs, or words in some formal language. A numbering can be used to transfer the idea of computability[1] and related concepts, which are originally defined on the natural numbers using computable functions, to these different types of objects.
Common examples of numberings include Gödel numberings in first-order logic, the description numbers that arise from universal Turing machines and admissible numberings of the set of partial computable functions.
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