Complete numbering
In computability theory complete numberings are generalizations of Gödel numbering first introduced by A.I. Mal'tsev in 1963. They are studied because several important results like the Kleene's recursion theorem and Rice's theorem, which were originally proven for the Gödel-numbered set of computable functions, still hold for arbitrary sets with complete numberings.Definition
A numbering of a set is called complete if for every partial computable function there exists a total computable function so that :
Ershov refers to the element a as a "special" element for the numbering. A numbering is called precomplete if the weaker property holds:Examples
