Productive Set
المؤلف:
Davis, M
المصدر:
Computability and Unsolvability. New York: Dover, 1982.Kleene, S. C. Mathematical Logic. New York: Dover, 2002.Rogers, H. Theory of Recursive Functions and Effective Computability. Cambridge, MA: MIT Press, 1987.
الجزء والصفحة:
...
20-1-2022
1338
Productive Set
A set 
of integers is productive if there exists a partial recursive function 
such that, for any 
, the following holds: If the domain of 
is a subset of 
, then 
is convergent, 
belongs to 
, and 
does not belong to the domain of 
, where 
denotes a recursive function whose Gödel number is 
.
Productive sets are not recursively enumerable.
REFERENCES
Davis, M. Computability and Unsolvability. New York: Dover, 1982.Kleene, S. C. Mathematical Logic. New York: Dover, 2002.Rogers, H. Theory of Recursive Functions and Effective Computability. Cambridge, MA: MIT Press, 1987.
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