Definition and Examples
A numbering of a set is a partial surjective function from to S (Ershov 1999:477). The value of a numbering ν at a number i (if defined) is often written ν'i instead of the usual .
For example, the set of all finite subsets of has a numbering γ in which and (Ershov 1999:477).
As a second example, a fixed Gödel numbering of the computable partial functions can be used to define a numbering W of the recursively enumerable sets, by letting by W(i) be the domain of φi.
Read more about this topic: Numbering (computability Theory)
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