Simple Theories
Seiten
2000
Springer (Verlag)
978-0-7923-6221-0 (ISBN)
Springer (Verlag)
978-0-7923-6221-0 (ISBN)
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.
Preface. Acknowledgements. 1. Preliminaries. 2. Simplicity. 3. Hyperimaginaries. 4. Groups. 5. Supersimple Theories. 6. Miscellaneous. Bibliography. Index.
| Erscheint lt. Verlag | 29.2.2000 |
|---|---|
| Reihe/Serie | Mathematics and Its Applications ; 503 | Mathematics and Its Applications ; 503 |
| Zusatzinfo | XIII, 260 p. |
| Verlagsort | Dordrecht |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 0-7923-6221-7 / 0792362217 |
| ISBN-13 | 978-0-7923-6221-0 / 9780792362210 |
| Zustand | Neuware |
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