User:IssaRice/Computability and logic/Comparison of concepts in computability theory

Set	Intuitive meaning	In terms of characteristic function
Primitive recursive set		The characteristic function (which must be a total function) is primitive recursive
Recursive set	Given any natural number, after a finite amount of time one can tell whether the number is in the set or not	The characteristic function (which must be a total function) is recursive
Semirecursive set	Given any natural number, if it is in the set, then after a finite amount of time one can tell that the number is in the set. If the number is not in the set, one never finds out.	The positive semicharacteristic function (which equals 1 if the given argument is in the set, and is undefined otherwise) is recursive.
Recursively enumerable set