  An inaccessible cardinal kappa is supercompact when (kappa, lambda)-ITP holds
for all lambda greater than or equal to kappa. We prove that if there is a
model of ZFC with infinitely many supercompact cardinals, then there is a model
of ZFC where for every natural number n greater than 1 and for every ordinal mu
greater than or equal to aleph_n, we have (aleph_n, mu)-ITP.
