Lecture Notes in Logic, 44

A Guide to NIP Theories

Pierre Simon

Year: 2015

166 pages. Hardcover.
Buy now (when ordering, include the discount code ASL2016 to receive the 25% ASL member discount)

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.

  • The first book devoted to NIP theories
  • A concise introduction that provides enough background material to understand current research in the area
  • Contains over 50 exercises and pointers to additional topics to help readers progress further

Table of Contents

  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