Automorphisms of First-Order Structures

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 Comprised of a collection of articles—some introductory, some more in-depth, and some containing previously unpublished research—the book will prove invaluable to graduate students meeting the subject for the first time as well as to active researchers studying mathematical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

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Product Details

  • ISBN-13: 9780198534686
  • Publisher: Oxford University Press, USA
  • Publication date: 8/28/1994
  • Series: Logic Guides Series
  • Pages: 400
  • Product dimensions: 6.31 (w) x 9.50 (h) x 1.11 (d)

Meet the Author

The University, Edgbaston, Birmingham

Queen Mary and Westfield College, London

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Table of Contents

List of contributors
Models and groups 3
Examples of N[subscript 0]-categorical structures 33
A survey of Jordan groups 73
The structure of totally categorical structures 111
Permutations and the axiom of choice 131
Relational structures and dimensions 153
Bases in permutation groups 181
Canonical expansions of countably categorical structures 199
Some combinatorial aspects of the cover problem for totally categorical theories 215
A generalization of Jordan groups 233
Recursive saturation 243
Indiscernibles 257
The small index property and recursively saturated models of Peano arithmetic 281
A Galois correspondence for countable recursively saturated models of Peano arithmetic 293
Stable groups 315
On generic normal subgroups 319
On Frobenius groups of finite Morley rank I 325
On Frobenius groups of finite Morley rank II 341
Bibliography 351
Index of notation 369
Index 373
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