Clones of inductive superpositions of terms

Abstract

<abstract><p>A superposition is an operation of terms by which we substitute each variable within a term with other forms of terms. With more options of terms to be replaced, an inductive superposition is apparently more general than the superposition. This comes with a downside that it does not satisfy the superassociative property on the set of all terms of a given type while the superposition does. A derived base set of terms on which the inductive superposition is superassociative is given in this paper. A clone-like algebraic structure involving such base set and superposition is the main topic of this paper. Generating systems of the clone-like algebra are characterized and it turns out that the algebra is only free with respect to itself under the certain selections of fixed terms concerning its inductive superposition or the specific type of its base set.</p></abstract>