On a family of precomplete classes of recursive functions and predicates (Q1916568)

One of the basic problems in the theory of functional systems is the problem of completeness. The present article is devoted to a functional system of one-place general recursive functions and predicates with program means of closure. The completeness of the set of functions and predicates in this system means the possibility to compute any general recursive function or predicate with the sole use of elements of this set. Starting with E. Post's work about the functions of two-valued logic, the traditional access to the completeness problem is given by description of all precomplete classes. In the present article we show that the preservation of ``belonging to an infinite sequence of sets'' leads to precomplete classes under appropriate choice of the sequence.