FRAGILE MEASURABILITY

Laver [L] and others [G-S] have shown how to make the supercompactness or strongness of kappa indestructible by a wide class of forcing noti ons. We show, alternatively, how to make these properties fragile. Spe cifically, we prove that it is relatively consistent that any forcing which preserves kappa(<kappa) and kappa+, but not P(kappa), destroys t he measurability of kappa, even if kappa, is initially supercompact, s trong, or if I1(kappa) holds. Obtained as an application of some gener al lifting theorems, this result is an ''inner model'' type of theorem proved instead by forcing.