  Just as Lascar's notion of abstract rank axiomatizes the U-rank, we propose
axioms for the ranks $SU^d$ and $SU^f$, the foundation ranks of dividing and
forking. We study the relationships between these axioms. As with superstable,
we characterize supersimple types and theories based on the existence of these
ranks. We show that the U-rank is the foundation rank of the Lascar-splitting
independence relationship. We also provide an alternative definition of SUd
similar to the original definition of U. Finally, we check that if in the
standard characterizations of simple and supersimple we change the non-forking
independence for the non-lascar-splitting independence, we characterize stable
and superstable.
