  Let k be a definable L-cardinal. Then there is a set of reals X,
class-generic over L, such that L(X) and L have the same cardinals, X has size
k in L(X) and some pi-1-2 formula defines X in all set-generic extensions of
L(X). Two corollaries, both assuming the consistency of an inaccessible: It is
consistent for the Perfect Set Property to hold for boldface sigma-1-2 sets,
yet fail for some lightface pi-1-2 set. It is consistent that the Perfect Set
Property holds for boldface sigma-1-2 sets yet some lightface pi-1-2
wellordering of some set of reals has length aleph-1000.
