Automorphisms of First-Order Structures [Hardcover]

This superb survey of the study of mathematical structures details how both model theoretic methods and permutation theoretic methods are useful in describing such structures. In addition, the book provides an introduction to current research concerning the connections between model theory and permutation group theory. Comprised of a collection of articles--some introductory, some more in-depth, and some containing previously unpublished research--the book will prove invaluable to graduate students meeting the subject for the first time as well as to active researchers studying mathematical logic and permutation group theory.

PART I: Automorphisms and Permutation Groups
1. Models and Groups
2. Examples of -Categorical Structures
3. A Survey of Jordan Groups
4. The Structure of Totally Categorical Structures
5. Permutations and the Axiom of Choice
6. Relational Structures and Dimensions
7. Bases in Permutation Groups
8. Canonical Expansions of Countably Categorical Structures
9. Some Combinatorial Aspects of The Cover Problem For Totally Categorical Theories
10. A Generalization of Jordan Groups
PART II: Recursively Saturated Models
11. Recursive Saturation
12. Indiscernibles
13. The Small Index Property and Recursively Saturated Models of Peano Arithmetic
14. A Galois Correspondence for Countable Recursively Saturated Models of Peano Arithmetic
PART III: Groups of Finite Morley Rank
15. Stable Groups
16. On Generic Normal Subgroups
17. On Frobenius Groups of Finite Morley Rank I
18. On Frobenius Groups of Finite Morley Rank II

An introduction to and a survey of several interrelated parts of model theory and the theory of permutation groups, supplemented by a numer of research papers in which the themes of the book are particularly prominent. . . .enhanced by the extensive and explicit cross-referencing between the various independently authorl°