 The first enrichment, standard possible worlds semantics, is introduced to explain the meaning of modal operators like ‘possible’ and ‘necessary’ and to distinguish the intuitive subject matter represented by particular subsentential expressions. Consider the expressions ‘Roger Federer’, ‘the greatest tennis player of all time’, and ‘the most famous Swiss citizen in 2020’. Let’s assume all three expressions happen to have exactly the same extension: a particular individual RF. So a simple extensional semantics will assign exactly the same semantic value to all three expressions. But clearly they differ in meaning: if events had unfolded only slightly differently than they actually did, the three expressions would pick out different people. In general, definite descriptions like ‘the greatest tennis player’ or ‘the most famous Swiss citizen’ pick out different individuals depending on who happens to have the relevant properties in counterfactual situations; whereas proper names like ‘Roger Federer’ rigidly pick out the very same individual in every possible  situation.[1]  [See entry on  rigid designators.]  Moreover, such differences in what expressions pick out in counterfactual situations affect the truth of modal claims: e.g., ‘Federer is necessarily Federer’ is true, but ‘Federer is necessarily the greatest tennis player’ is false. So there is an aspect of meaning that is not captured in simple extensional semantics. The basic idea behind possible world semantics is to map out such differences in meaning by specifying what an expression picks out relative to every possible way the world could be (every “possible world”).