The review presents general methods for constructing bases under superpositions (finite or infinite) in the class of total functions. We establish a criterion for existance of bases in □²-closed classes in terms of maximally universal functions. Various examples of bases in the class of Kalmar elementary functions are presented. We prove that every countable class closed under primitive recursion has an infinite basis under superposition. The obtained general theorems bind the existance of bases under superposition in classes of single variable and multiple variable functions.

bases under superposition, classes of recursive functions

Mathematical problems and theory of numerical methods