CLONE OF LINEAR TERMS AND CLONE OF LINEAR FORMULAS

Abstract

Terms and formulas are expressed in a first-order language which are used to describe properties of algebraic systems consisting a non-empty set together with a sequence of operations and a sequence of relations on this set. In this paper we study on linear terms of type (n) for a natural number n>1, this leads to define the definition of linear formulas of type ((n),(m)) for natural numbers n,m > 1. To construct clone of linear terms and clone of linear formulas we give a new concept of the partial superposition operation of linear terms and the partial superposition operation of linear formulas, respectively. Moreover, we show that both of them are satisfied the superassociative law and the extension of a many-sorted mapping, which maps a generating system to clone, is an endomorphism.