  Remarkably, it turns out that when one restricts to those theories that “arise in nature” the interpretability ordering is quite simple: There are no descending chains and there are no incomparable elements—the interpretability ordering on theories that “arise in nature” is a wellordering.  In particular, although there are natural examples of the first and second kind of independence (e.g. PM and CH, respectively, something to which we will return to below), there are no known natural examples of the third kind of independence.