Each interpretation is a point in model space.
Sentences divide space of all models.
There are models that cannot be distinguished by any set of sentences. There is a simple representative for any indistinguishable set of models. The set of all partial orders is a relational class. Note that we can write an infinite theory that has only infinite models. If a set of sentences has a model of any infinite cardinality, then it has a model of every infinite cardinality.