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＜電子ブック＞
Simple Theories / by Frank O. Wagner
(Mathematics and Its Applications ; 503)

版	1st ed. 2000.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2000
本文言語	英語
大きさ	XIII, 260 p : online resource
著者標目	*Wagner, Frank O author SpringerLink (Online service)
件　名	LCSH:Mathematical logic LCSH:Group theory LCSH:Commutative algebra LCSH:Commutative rings FREE:Mathematical Logic and Foundations FREE:Group Theory and Generalizations FREE:Commutative Rings and Algebras
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-94-017-3002-0

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