  It is worth contrasting the behaviour of the sentence B and the sentence A0. From the ω+1st stage on, B is stabilizes as true. In fact, B is stably true in every revision sequence for M. Thus, B is categorically true in M. The sentence A0, however, never quite stabilizes: it is usually true, but within a few finite stages of a limit ordinal, the sentence A0 can be false. In these circumstances, we say that A0 is nearly stably true (See Definition 3.10, below.) In fact, A0 is nearly stably true in every revision sequence for M. □ 