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Simple Theories
Mathematics and Its Applications 503
ISBN/EAN: 9789048154173
Umbreit-Nr.: 973576
Sprache:
Englisch
Umfang: xiii, 260 S.
Format in cm:
Einband:
kartoniertes Buch
Erschienen am 15.12.2010
Auflage: 1/2000
- Zusatztext
- 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.