Defining 'isomorphic'.

     "Z/2 (`integers mod 2'), with + and *,
         is isomorphic to 
      Booleans with XOR and AND."

     Def'n of "two structures are isomorphic":
       [First: a `structure' is just `an interpretation' -- that is,
        a domain, and relations/functions on that domain.]
     We say that two structures are isomorphic if there is a bijection
     which preserves the relations.

     Another example: 
      Consider polyhedra, which have vertices, edges, and faces.
      The statement "the cube is the dual of the octahedron" means:
         an octahedron, with relations <isAFace,isAnEdge,isAVertex,isAdjacent>
     is isomorphic to
         a cube,        with relations <isAVertex,isAnEdge,isAFace,isAdjacent>.
     (Note that we're using the same relations but in a different *order* --
      unlike the Z/2 vs Booleans, where the relations weren't shared.)

     This harks back to interpretations: "Any statement true of a cubes using
       those relations is also true about octohedra using the 
       relations in the new order"
     Interestingly, this is not restricted to a first-order-logic statements,
     but *any* statement!