Simple Theories / by Frank O. Wagner.

Format:

Book

Author/Creator:

Wagner, Frank O., Author.

Series:

Mathematics and Its Applications ; 503

Language:

English

Subjects (All):

Logic, Symbolic and mathematical.

Group theory.

Commutative algebra.

Commutative rings.

Mathematical Logic and Foundations.

Group Theory and Generalizations.

Commutative Rings and Algebras.

Local Subjects:

Mathematical Logic and Foundations.

Group Theory and Generalizations.

Commutative Rings and Algebras.

Physical Description:

1 online resource (XIII, 260 p.)

Edition:

1st ed. 2000.

Place of Publication:

Dordrecht : Springer Netherlands : Imprint: Springer, 2000.

Summary:

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.

Notes:

Includes bibliographical references and index.

ISBN:

94-017-3002-4