 A graph extended with set parameters  (or extended graph for short) is a set G  together with a function   e: G→       ℘G+V.  If  e(g)    is of the form   ⟨s,0⟩   for some s ⊆ G, then  we intend it as a node just as in our earlier treatment.    In particular, we want to decorate it with the set of decorations of its children.   If  e(g) =  ⟨x,1⟩ ,  then we want a decoration to be forced to have the value x on g.   