 We start below with a subsection on models that can be characterized in second-order logic by one sentence up to isomorphism. Another approach to the model theory of second-order logic is to focus on models with large cardinal (inaccessible, measurable, supercompact cardinals) properties. This is the topic of  §7.2.  Finally, in  §7.3  we consider the possibility of allowing the so-called general models introduced in  §9.1.  In this case second-order logic becomes very much like first order logic. However, general models are mostly interesting when they are so-called Henkin models, i.e., they satisfy the so-called Comprehension Axioms. In Henkin models second-order logic satisfies the Compactness Theorem and other principles familiar from first order model theory but no general structure- or classification theory exists yet, perhaps because the Comprehension Axioms bring in a lot of complicated structure into the models.