Some points of clarification: first, the definitions above involve quantification over properties and hence higher-order logic. Second, in (1), expressions of the form formula_3 capture the concept of sharing all properties, or being indiscernible with respect to a set of properties. Thus, (1) can be understood more intuitively as the claim that all objects that are indiscernible with respect to a base set of properties are indiscernible with respect to a supervenient set of properties, or, as it is also sometimes said, that B-twins are A-twins. Finally, supervenience claims typically involve some modal force, however, the way that modal force is specified depends on which more specific variety of supervenience one decides upon (see below).