Automorphisms of first-order structures

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Bibliographic Information

Automorphisms of first-order structures

edited by Richard Kaye and Dugald Macpherson

Clarendon Press , Oxford University Press, 1994

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Includes bibliographical references and indexes

Description and Table of Contents

Description

This book is a collection of articles, some introductory, some extended surveys, and some containing previously unpublished research, on a range of topics linking infinite permutation group theory and model theory. Topics covered include: oligomorphic permutation groups and omega-categorical structures; totally categorical structures and covers; automorphism groups of recursively saturated structures; Jordan groups; Hrushovski's constructions of pseudoplanes; permutation groups of finite Morley rank; applications of permutation group theory to models of set theory without the axiom of choice. There are introductory chapters by the editors on general model theory and permutation theory, recursively saturated structures, and on groups of finite Morley rank. The book is almost self-contained, and should be useful to both a beginning postgraduate student meeting the subject for the first time, and to an active researcher from either of the two main fields looking for an overview of the subject.

Table of Contents

  • I. Automorphisms and Permutation Groups
  • Models and groups
  • Examples of -categorical structures
  • A survey of Jordan groups
  • The structure of totally categorical structures
  • Permutations and the axiom of choice
  • Relational structures and dimensions
  • Bases in permutation groups
  • Canonical expansions of countably categorical structures
  • Some combinatorial aspects of the cover problem for totally categorical theories
  • A generalization of Jordan groups
  • Recursive saturation
  • Indiscernibles
  • The small index property and recursively saturated models of Peano arithmetic
  • A Galois correspondence for countable recursively saturated models of Peano arithmetic
  • Stable groups
  • On generic normal subgroups
  • On Frobenius groups of finite Morley rank I
  • On Frobenius groups of finite Morley rank II
  • Bibliography
  • Index of notation
  • Index
  • Acknowledgements

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