  Many of the most common reverse Easton iterations found in the large cardinal
context, such as the Laver preparation, admit a gap at some small delta in the
sense that they factor as P*Q, where P has size less than delta and Q is forced
to be delta-strategically closed. In this paper, generalizing the Levy-Solovay
theorem, I show that after such forcing, every embedding j:V[G]-->M[j(G)] in
the extension which satisfies a mild closure condition is the lift of an
embedding j:V-->M in the ground model. In particular, every ultrapower
embedding in the extension lifts an embedding from the ground model and every
measure in the extension which concentrates on a set in the ground model
extends a measure in the ground model. It follows that gap forcing cannot
create new weakly compact cardinals, measurable cardinals, strong cardinals,
Woodin cardinals, strongly compact cardinals, supercompact cardinals, almost
huge cardinals, huge cardinals, and so on.
