Further Completeness Criteria

Abstract

In the literature, one finds many articles which deal with complete sets. With the aid of complete sets, it is easy to obtain completeness criteria. In this chapter, we discuss only three types of such criteria. First we handle a criterion for Sheffer functions, which was found by G. Rousseau. Then, we show how one can reduce the conditions from Theorem 6.1 if one considers only surjective functions. Finally, we deal with criteria that indicate under which conditions a set ($\subseteq$ P_k) which consists of certain unary functions and a Słupecki-function is complete in P_k.