computable function

…truth: that all recursive or computable functions and relations are representable in the system (e.g., in N). Since truth in the language of a system is itself not representable (definable) in the system, it cannot, by the lemma, be recursive (i.e., decidable).

, of being effectively—or mechanically—calculable. Functions that can be so calculated are called recursive. Several different and historically independent attempts have been made to define the class of all recursive functions, and these have turned out to coincide with each other. The claim that recursive functions exhaust the class…

…led to the theory of computable functions, which governs those functions that can be calculated by a digital computer. Kleene was the author of Introduction to Metamathematics (1952) and Mathematical Logic (1967).