Finite Model Theory: Second Edition

This volume presents the main results of descriptive complexity theory: the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. Important logics in this context include fixed-point logics, transitive closure logics, and also certain infinitary languages. Other topics include DATALOG languages, quantifiers and oracles, 0-1 laws, and optimization and approximation problems. The book is written in such a way that the respective parts on model theory and descriptive complexity theory may be read independently. This second edition is a thoroughly revised and enlarged version of the original text.