 Second, we consider Fa = (S × a)   + 1. Here 1 = {0} and + is the disjoint union operation.   However, it is  more common for people to represent the one and only element of  1 using a symbol like *. The coalgebras are like stream systems of equations, except now an equation might ask for a stream to “stop” by having * on the right-hand  side. So an example of a coalgebra would be  x ≈  ⟨s,y⟩ ,  y ≈ *. Then the solution would  take  x†  to be the one-term sequence  s. The logic for this functor would be the same logic (HML) as before, except that now we add an atomic sentence to detect the ends of finite sequences.  