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Simple Theories

  • Book
  • © 2000

Overview

Authors:
  1. Frank O. Wagner

    1. Institut Girard Desargues, Université Claude Bernard (Lyon-1), Villeurbanne, France

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Part of the book series: Mathematics and Its Applications (MAIA, volume 503)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xi
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  2. Preliminaries

    • Frank O. Wagner
    Pages 1-14

  3. Simplicity

    • Frank O. Wagner
    Pages 15-50

  4. Hyperimaginaries

    • Frank O. Wagner
    Pages 51-93

  5. Groups

    • Frank O. Wagner
    Pages 95-145

  6. Supersimple Theories

    • Frank O. Wagner
    Pages 147-186

  7. Miscellaneous

    • Frank O. Wagner
    Pages 187-243

  8. Back Matter

    Pages 245-260
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Keywords

About this book

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.

Authors and Affiliations

  • Institut Girard Desargues, Université Claude Bernard (Lyon-1), Villeurbanne, France

    Frank O. Wagner

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