Bibliographic Information

Simple theories

by Frank O. Wagner

(Mathematics and its applications, v. 503)

Kluwer Academic, c2000

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Note

Includes bibliographical references and index

Description and Table of Contents

Description

Simplicity theory is an extension of stability theory to a wider class of structures, containing, among others, the random graph, pseudo-finite fields, and fields with a generic automorphism. Following Kim's proof of `forking symmetry' which implies a good behaviour of model-theoretic independence, this area of model theory has been a field of intense study. It has necessitated the development of some important new tools, most notably the model-theoretic treatment of hyperimaginaries (classes modulo type-definable equivalence relations). It thus provides a general notion of independence (and of rank in the supersimple case) applicable to a wide class of algebraic structures. The basic theory of forking independence is developed, and its properties in a simple structure are analyzed. No prior knowledge of stability theory is assumed; in fact many stability-theoretic results follow either from more general propositions, or are developed in side remarks. Audience: This book is intended both as an introduction to simplicity theory accessible to graduate students with some knowledge of model theory, and as a reference work for research in the field.

Table of Contents

Preface. Acknowledgements. 1. Preliminaries. 2. Simplicity. 3. Hyperimaginaries. 4. Groups. 5. Supersimple Theories. 6. Miscellaneous. Bibliography. Index.

by "Nielsen BookData"

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Details

  • NCID
    BA46510042
  • ISBN
    • 0792362217
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Dordrecht ; Boston
  • Pages/Volumes
    xi, 260 p.
  • Size
    25 cm
  • Parent Bibliography ID
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