There are also several kinds of global supervenience relations, which were introduced to handle cases in which worlds are the same at the base level and also at the supervenient level, but where the ways the properties are connected and distributed in the worlds differ. For example, it is consistent with global mental–physical supervenience on the simple formulation described above for two worlds to have the same number of people in the same physical states, but for the mental states to be distributed over those people in different ways (e.g. I have my father's thoughts in the other world, and he has my thoughts). To handle this, property-preserving isomorphisms (1-1 and onto functions between the objects of two worlds, whereby an object in one world has a property if and only if the object which that function takes you to in the other world does) are used, and once this is done, several varieties of global supervenience can be defined.