Closed classes of ultimately periodic functions (Q2773677)

The author introduces the concept of a recursively closed set and gives a description of recursively closed classes generated by constants. To this end, the author defines the notion of an ultimately periodic function which generalizes that of a periodic function. He proves that a recursively closed class generated by a set of \(n\) constants coincides with the class of all ultimately periodic functions whose periods divide natural degrees of the number \(n!\) and whose values belong to the set of constants. This implies that the recursively closed class generated by all constants is equal to the class of all ultimately periodic functions.