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.
| Autorius: | Frank O. Wagner |
| Serija: | Mathematics and Its Applications |
| Leidėjas: | Springer Netherlands |
| Išleidimo metai: | 2000 |
| Knygos puslapių skaičius: | 276 |
| ISBN-10: | 0792362217 |
| ISBN-13: | 9780792362210 |
| Formatas: | Knyga kietu viršeliu |
| Kalba: | Anglų |
| Žanras: | Mathematical logic |
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