 Theorem (van Ditmarsch and Kooi 2006). The preserved formulas are formed by the following grammar.  \[\begin{gather*} F \ccoloneqq p \mid \lnot p \mid F\land F \mid F\lor F\mid [a]F\mid [\lnot F!]F \mid [B*]F \\ \small p\in\sP,\; a\in\sA,\; B\subseteq\sA \end{gather*}\]   Every preserved formula is successful.