 Direct conversion of structures (from \(\SOL\) to \(\MSL^{\SOL}\)): Let us define \(\Conv_{1}\) as a function which takes any structure \(\mathcal{A}\in\Str(\SOL)\) and returns a structure \(\mathcal{A}^{\ast}\in \Str(\MSL^{\SOL})\). These structures are basically the same, with the only exception of membership relations we now add. This membership relation symbol of the many-sorted language, \(\epsilon _{n}\), is interpreted as genuine membership,