A Guide to NIP Theories

The first book to introduce the rapidly developing subject of NIP theories, for students and researchers in model theory.

Pierre Simon (Author)

9781107057753, Cambridge University Press

Hardback, published 16 July 2015

166 pages, 50 exercises
23.6 x 16 x 1.8 cm, 0.4 kg

'This book presents NIP theories as a rich and coherent subject, showing a field with a considerable degree of development, particularly taking into account how recent most of the results are. Also, the author made a clear effort in presenting the most elegant proofs he could find, making this a very valuable book and accessible for any reader who understands model theory …' Alf Onshuus, Mathematical Reviews

The study of NIP theories has received much attention from model theorists in the last decade, fuelled by applications to o-minimal structures and valued fields. This book, the first to be written on NIP theories, is an introduction to the subject that will appeal to anyone interested in model theory: graduate students and researchers in the field, as well as those in nearby areas such as combinatorics and algebraic geometry. Without dwelling on any one particular topic, it covers all of the basic notions and gives the reader the tools needed to pursue research in this area. An effort has been made in each chapter to give a concise and elegant path to the main results and to stress the most useful ideas. Particular emphasis is put on honest definitions, handling of indiscernible sequences and measures. The relevant material from other fields of mathematics is made accessible to the logician.

1. Introduction
2. The NIP property and invariant types
3. Honest definitions and applications
4. Strong dependence and dp-ranks
5. Forking
6. Finite combinatorics
7. Measures
8. Definably amenable groups
9. Distality
Appendix A. Examples of NIP structures
Appendix B. Probability theory
References
Index.

Subject Areas: Mathematical modelling [PBWH], Mathematical logic [PBCD], Mathematics [PB]