The link between modal logic and non-well-founded sets has been shown by P. Aczel [1988], and systematically by J. Barwise and L. Moss [1996]. A. Baltag [1998] also proved some important theorems about characterizing sets by modal sentences. The aim of this paper is to explore the relationship between modal logic and sets more deeply in the expressive power of modal languages and modal definability over sets. Let’s consider both basic and infinitary modal languages.