Simple Theories
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.
1117397243
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.
Simple Theories
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.
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.
54.99
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Simple Theories
260
Simple Theories
260Paperback(Softcover reprint of hardcover 1st ed. 2000)
$54.99
54.99
In Stock
Product Details
| ISBN-13: | 9789048154173 |
|---|---|
| Publisher: | Springer Netherlands |
| Publication date: | 12/09/2010 |
| Series: | Mathematics and Its Applications , #503 |
| Edition description: | Softcover reprint of hardcover 1st ed. 2000 |
| Pages: | 260 |
| Product dimensions: | 6.10(w) x 9.25(h) x 0.02(d) |
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