the image of a computable set under a computable function is c.e., but possibly not computable). A is a computable set if and only if it is at level of the arithmetical hierarchy. A is a computable set if and only if it is either the range of a nondecreasing total computable function, or the empty set. The image of a computable set under a nondecreasing total computable function is computable. See also Recursively enumerable language Recursive language Recursion References Cutland, N. Computability. Cambridge University Press, Cambridge-New York, 1980. ; Rogers, H. The Theory of Recursive Functions and Effective Computability, MIT Press. ; Soare, R. Recursively enumerable sets and degrees. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, 1987. External links Computability theory Theory of computation