 But recent developments in inner model theory (due to Woodin) show that everything changes at the level of a supercompact cardinal. These developments show that if there is an inner model N which “inherits” a supercompact cardinal from V (in the manner in which one would expect, given the trajectory of inner model theory), then there are two remarkable consequences: First, N is close to V (in, for example, the sense that for sufficiently large singular cardinals λ, N correctly computes λ+). Second, N inherits all known large cardinals that exist in V. Thus, in contrast to the inner models that have been developed thus far, an inner model at the level of a supercompact would provide one with an axiom that could not be refuted by stronger large cardinal assumptions. 