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 natu

ral 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 superpo

sition 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.