 Correspondence results allow us to distinguish by modal means a number of class of frames. However expressivity of the modal operators strongly limit the capacity of the language to discern classes of structures. To this extent the reader should notice that the logics of both playable and truly playable effectivity frames share the fact that \(\models_F [\emptyset]\top\). However this proposition, whose interpretation is that for each \(w\in W, \{W\} \in E_w(\emptyset)\), is not sufficient to make a formal distinction between \(E_w(\emptyset)\) in the two different classes of effectivity functions.