A compactification of the algebra of terms

Abstract

Let o-:S--->to be a similarity type, i.e., S is a set of funct ion symbols, to ={0, 1 ,2 . . . . } and for every FeS , o-(F) is the rank of F. Let us assume for a while that o'(F) = 0 for some F e S (such F are called constant symbols*). Let Q~ denote the set of all constant terms, i.e., the smallest set such that { F e S: o(F)= 0}_ Q~ and F-r~ 9 9 9 ~'~<~)e Q~, for every F e S and r 1 . . . . . Ttr(F)~ Q~. We put