Existentially Closed Groups [Hardcover]

In this volume, the authors introduce the theory of existentially closed groups, bringing together both well-established and more contemporary ideas, interpretations, and proofs. They adopt a group-theoretical rather than a model-theoretical point of view as they define existentially closed groups and summarizes some of the techniques that are basic to infinite group theory, such as the formation of free products with amalgamation and HNN-extensions. From this basis the theory is developed and many of the more recently discovered results are proved and discussed.

1. Introduction
2. Centralizers and Normalizers of Subgroups
3. Homogenous Groups
4. Recursion Theory
5. Applications of the Subgroup Theorem
6. The Relative Subgroup Theorem
7. Games
8. Free Products
9. First-Order of Existentially Closed Groups
9.1. Introduction
9.2. Existentially Closed Groups and First-Order Theory
9.3. Stable Evaluation
9.4. Arithmetically Related Groups
9.5. Generic Theory

The text is well written and accessible to anyone with some basic knowledge of group theory and logic. --American Mathematical Monthly