 However, the formula \([p!]\lnot[\{a,b\}*][a]p\) is false at \((M,w)\) because, after the announcement of p, the model \(M[p!]\) pictured in Figure 2 obtains, and all worlds in this model are \([a]p\)-worlds. In fact, whenever p is true, the formula \([p!]\lnot[\{a,b\}*][a]p\) is always false: after the announcement of p, all that remains are p-worlds, and therefore every world is an \([a]p\)-world. 