 With these tools, it is now possible to make precise the claim that the situation described above cannot be represented. A language is said to be complete for a belief model if and only if every possible statement in a player’s language (i.e., every statement in her language that is true in at least one state) can be assumed by the player. It is then possible to show, using a diagonal argument, that no belief model is complete for ‘its first-order language’, i.e., the language containing all first-order definable subsets of the model’s domain.