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Automorphisms of First-order Structures : Oxford Logic Guides - Richard Kaye

Automorphisms of First-order Structures

Oxford Logic Guides

Hardcover

Published: 11th August 1994
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This book is a collection of articles, some introductory, some extended surveys, and some containing previously unpublished research, on a range of topics linking infinite permutation group theory and model theory.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.

"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 "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 "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 "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 thevarious 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

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 II Recursively Saturated Models: 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 III Groups of Finite Morley Rank: 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

ISBN: 9780198534686
ISBN-10: 019853468X
Series: Oxford Logic Guides
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 400
Published: 11th August 1994
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 24.1 x 16.1  x 2.8
Weight (kg): 0.74