  Let kappa be the limit of <kappa_n : n<omega> (1) if each kappa_n carries an
extender of the length of the first Mahlo above kappa_n, then for every ld
above kappa there is a generic extension with power of kappa above ld. (2) if
each kappa_n carries an extender of the length of the first fixed point of the
aleph function above kappa_n of order n then for every ld between kappa and the
first inaccessible above kappa there is a generic extension satisfying
2^kappa>ld.
