Indescribable cardinals without diamonds

where E is a stationary subset of some cardinal ~. Jensen (cf. I-D2]) showed that if K is regular and uncountable and V=L then O~,E holds. Following his work, a number of applications of this principle and its modifications have been developed which are wide ranging and not restricted to set theory (cf. [-D1]). Jensen had also discovered that various large cardinals carry diamond sequences with them; for example if ~c is ineffable or even if x is subtle (see [D2] and [KM] for the definitions of these concepts) then O~,R~gn~ holds (where Reg denotes the class of all regular cardinals). It has been asked by several people whether cardinals below the least subtle cardinal carry diamond sequences. In this paper we show that it is consistent that C'~,R~0~ fails at a/7,"(m > 1, n > 1) indescribable cardinal x. Assuming that ~ is/7~' indescribable, we shall work in L and define an iteration P of length ~c + 1 which at stage 2 < ~: kills off all candidates for O z. ~eo~z sequences. In order to show that P preserves the H~ indescribability of ~ we use the elementary embedding characterization of/7~ indeseribability in [H 1] and master condition arguments. P will preserve all cofinalities and not add too many sets. Thus we obtain