Automorphisms of First-Order Structures by Richard KayeAutomorphisms of First-Order Structures by Richard Kaye

Automorphisms of First-Order Structures

byRichard Kaye, Dugald Macpherson

Hardcover | June 1, 1993

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This book is a collection of articles, some introductory, some extended surveys, and some containing previously unpublished research, on a range of topics linking infinite permutation group theory and model theory.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-categoricalstructures; 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 ofchoice. 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 firsttime, and to an active researcher from either of the two main fields looking for an overview of the subject.
Richard Kaye is at The University, Edgbaston, Birmingham. Dugald Macpherson is at Queen Mary and Westfield College, London.
Title:Automorphisms of First-Order StructuresFormat:HardcoverDimensions:400 pages, 9.21 × 6.14 × 1.1 inPublished:June 1, 1993Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:019853468X

ISBN - 13:9780198534686

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Table of Contents

I. Automorphisms and Permutation GroupsModels and groupsExamples of -categorical structuresA survey of Jordan groupsThe structure of totally categorical structuresPermutations and the axiom of choiceRelational structures and dimensionsBases in permutation groupsCanonical expansions of countably categorical structuresSome combinatorial aspects of the cover problem for totally categorical theoriesA generalization of Jordan groupsII Recursively Saturated Models. Recursive saturationIndiscerniblesThe small index property and recursively saturated models of Peano arithmeticA Galois correspondence for countable recursively saturated models of Peano arithmeticIII Groups of Finite Morley Rank. Stable groupsOn generic normal subgroupsOn Frobenius groups of finite Morley rank IOn Frobenius groups of finite Morley rank IIBibliographyIndex of notationIndexAcknowledgements

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 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