# Complete numbering

### recursion theory

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1. ## In computability theory complete numberings are generalizations of Gödel numbering first introduced by A.I. Mal'tsev in 1963

created by factobot on March 2, 2009
2. ## 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

created by factobot on March 2, 2009
3. ## A numbering \nu of a set A is called complete (with respect to an element a ∈ A) if for every partial computable function f there exists a total computable function h so that ≦ft\ \beginmatrix \nu ° f(i) &\mboxif\ i ∈ \mathrmdom(f), \\ a &\mbo

created by factobot on March 2, 2009
4. ## \endmatrix \right

created by factobot on March 2, 2009
5. ## The numbering \nu is called precomplete if

created by factobot on March 2, 2009
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