Bounded Variable Logics and Counting: A Study in Finite Models (Lecture Notes in Logic)

This monograph in finite model theory offers a comprehensive treatment of a variety of results in the model theory and descriptive complexity theory of infinitary logics with a bounded number of variables and logics with counting constructs.
The exposition is largely self-contained, with introductory sections on the relevant logics, model theoretic concepts, and the programme of descriptive complexity.