A Guide to NIP Theories 1st Edition by Pierre Simon 1107057752 ‎9781107057753

A Guide to NIP Theories 1st Edition by Pierre Simon – Ebook Instant Download/Delivery ISBN(s): 1107057752 ‎9781107057753

Product details:

• ISBN-10 ‏ : ‎ 1107057752
• ISBN-13 ‏ : ‎ 9781107057753
• Author: Pierre

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.

Table of contents:

CHAPTER 1 – INTRODUCTION

CHAPTER 2 – THE NIP PROPERTY AND INVARIANT TYPES

CHAPTER 3 – HONEST DEFINITIONS AND APPLICATIONS

CHAPTER 4 – STRONG DEPENDENCE AND DP-RANKS

CHAPTER 5 – FORKING

CHAPTER 6 – FINITE COMBINATORICS

CHAPTER 7 – MEASURES

CHAPTER 8 – DEFINABLY AMENABLE GROUPS

CHAPTER 9 – DISTALITYAPPENDIX A – EXAMPLES OF NIP STRUCTURES

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