Mathematics and Its Applications

Simple Theories

Authors: Wagner, Frank Olaf

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  • ISBN 978-0-7923-6221-0
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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.

Buy this book

Hardcover $109.00
price for USA
  • ISBN 978-0-7923-6221-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-90-481-5417-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Simple Theories
Authors
Series Title
Mathematics and Its Applications
Series Volume
503
Copyright
2000
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
Hardcover ISBN
978-0-7923-6221-0
Softcover ISBN
978-90-481-5417-3
Edition Number
1
Number of Pages
XIII, 260
Topics