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