Terms Over Many Sorted Universal Algebra

Let I be a non empty set, let X be a non-empty many sorted set indexed by I, and let i be an element of I. Note that X(i) is non empty. In the sequel S will be a non void non empty many sorted signature and V will be a non-empty many sorted set indexed by the carrier of S. Let us consider S, V . The functor S -Terms(V ) yielding a non empty subset of FinTrees(the carrier of DTConMSA(V )) is defined as follows: (Def.1) S -Terms(V ) = TS(DTConMSA(V )). Let us consider S, V . A term of S over V is an element of S -Terms(V ). In the sequel A denotes an algebra over S and t denotes a term of S over V . Let us consider S, V and let o be an operation symbol of S. Then Sym(o, V ) is a nonterminal of DTConMSA(V ). Let us consider S, V and let s1 be a nonterminal of DTConMSA(V ). A finite sequence of elements of S -Terms(V ) is called an argument sequence of s1 if: This article has been prepared during the visit of the author in Nagano in Summer 1994.