Types of Numberings
A numbering is total if it is a total function. If the domain of a partial numbering is recursively enumerable then there always exists an equivalent total numbering (equivalence of numberings is defined below).
A numbering η is decidable if the set is a decidable set.
A numbering η is single-valued if η(x) = η(y) if and only if x=y; in other words if η is an injective function. A single-valued numbering of the set of partial computable functions is called a Friedberg numbering.
Read more about this topic: Numbering (computability Theory)
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