This book contains an introduction to classical fundamental branches of mathematical logic: propositional and first-order topics, including a part of a basic model theory and Gödel’s incompleteness theorems. Moreover, we can find here three further subjects: Computability and complexity (chapter 7), Beyond first-order logic (chapter 9) and Finite model theory (chapter 10). The book is therefore useful for students of mathematics, computer science and logic. In the last section of the chapter Models of countable theories, the author gives an overview of concepts and results of modern model theory. A finite model theory is treated in the last chapter and apart from other things, some connections with problems of complexity theory are presented here. The book contains many examples and appropriate exercises and offers an inspiration in many directions

Reviewer:

jmk