Simple Theories

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Free Download Simple Theories  By  Frank Olaf Wagner
2000 | 260 Pages | ISBN: 0792362217 | PDF | 12 MB
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.

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