  The landmark Levy-Solovay Theorem limits the kind of large cardinal
embeddings that can exist in a small forcing extension. Here I announce a
generalization of this theorem to a broad new class of forcing notions. One
consequence is that many of the forcing iterations most commonly found in the
large cardinal literature create no new weakly compact cardinals, measurable
cardinals, strong cardinals, Woodin cardinals, strongly compact cardinals,
supercompact cardinals, almost huge cardinals, huge cardinals, and so on.
