Structure of program-closed classes of many-placed functions and predicates (Q1901952)

In Lect. Notes Comput. Sci. 278, 409-411 (1987; Zbl 0645.03047), we defined the structure \(\mathcal S\) of program-closed classes of one-place everywhere defined functions and predicates. As a tool of closure, there was chosen a certain class of program schemes with massives (arrays) and with verification of equalling of variables. As is known [see \textit{A. J. Kfoury}, Theor. Comput. Sci. 25, 1-66 (1983; Zbl 0499.68009)], this class differs from other ones by the property of universality (at least, among determinated consecutive program schemes). The structure \(\mathcal S\) arises as a result of ordering of closed classes with respect to inclusion. In the present article we introduce the structure \({\mathcal S}_M\) of classes of many-placed everywhere defined functions and predicates (closed with respect to the same class of program schemes and with the same order relation) and start its investigation.