 The semantics of  announcement updates  works by trimming models. \(!\varphi\) transforms a model M into a sub-model \(M_{|\varphi}\) consisting of all those points in M that satisfy \(\varphi\), while deleting all \(\neg\varphi\) nodes. Relations on \(M_{|\varphi}\) are those inherited from M. Crucially, deletion may change the truth value of formulas: after announcing \(!\varphi\), some nodes in \(M_{|\varphi}\) may satisfy \(\neg\varphi\). In particular, with M the set of points in a game tree, the set of available histories may keep shrinking as successive announcements are made. Hence, repeated announcements of \(!\rat \) make sense. In finite games, this process always reaches a limit, a smallest subgame where no move is dominated by another.