Automorphisms of First-Order Structures

by Richard Kaye, Dugald Macpherson

Overview

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 Comprised of a collection of articles—some introductory, some more in-depth, and some containing previously unpublished research—the book will prove invaluable to graduate students meeting the subject for the first time as well as to active researchers studying mathematical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.

Product Details

ISBN-13:	9780198534686
Publisher:	Oxford University Press
Publication date:	10/06/1994
Series:	Logic Guides Series
Pages:	400
Product dimensions:	9.21(w) x 6.14(h) x 0.94(d)

About the Author

The University, Edgbaston, Birmingham

Queen Mary and Westfield College, London

Table of Contents

PART I: Automorphisms and Permutation Groups1. Models and Groups2. Examples of -Categorical Structures3. A Survey of Jordan Groups4. The Structure of Totally Categorical Structures5. Permutations and the Axiom of Choice6. Relational Structures and Dimensions7. Bases in Permutation Groups8. Canonical Expansions of Countably Categorical Structures9. Some Combinatorial Aspects of The Cover Problem For Totally Categorical Theories10. A Generalization of Jordan GroupsPART II: Recursively Saturated Models11. Recursive Saturation12. Indiscernibles13. The Small Index Property and Recursively Saturated Models of Peano Arithmetic14. A Galois Correspondence for Countable Recursively Saturated Models of Peano ArithmeticPART III: Groups of Finite Morley Rank15. Stable Groups16. On Generic Normal Subgroups17. On Frobenius Groups of Finite Morley Rank I18. On Frobenius Groups of Finite Morley Rank II

Editorial Reviews

"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 authored chapters, and a very well-designed index. . . .It provides a sketch of the model theorist's current interpretation of the idea that mathematics is, among other things, the study of symmetry."—Journal of Symbolic Logic

From the Publisher