Descriptive Complexity Theory
Descriptive Complexity Theory is a branch of Complexity Theory and Finite Model Theory that characterizes complexity classes that need the type of logic.
The connection between logic on finite models allows results to be transferred from one area to another allowing new proof methods.
This also suggests that the common complexity classes are not dependent on the arbitrary computation models.
Specifically each logic prescribes a set of queries that can be stated in them, which represent computation problems when restricted to finite models.