Lubarsky - Kripke Models: Better Than Topological Models?

Since every Kripke model is a topological model (using an Alexandrov topology), when coming up with examples one might expect there to be a disadvantage in restricting attention to this sub-class. After all, wouldn't one be less able to develop a model with certain desired properties if one considers fewer models? In practice, though, the exact opposite is true. Topological models as such are always of a very limited kind in the literature, whereas Kripke models display a wide variety of construction techniques. I will demonstrate this by sketching several different specific Kripke models, with an emphasis in each case on something distinctive about their construction. I hope this will stimulate somebody either to explain why they have this additional flexibility over more general topological models or to show that they don't by exhibiting (non-Alexandrov) topological models with similarly varied constructions.