A Guide to NIP Theories
By Pierre Simon. 2012
304 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d9e90c32532ae221b2d659394c9c8effc330a187
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Citations in the corpus
- Definably amenable NIP groups (2015, background): “In the past ten or fifteen years, the role of NIP theories has grown to become a central notion in model theory thanks to applications to o-minimal structures, valued fields and combinatorics (see e.g. [Sim15a] or [Sta16] for a survey). Typical examples of NIP structures are given by stable structures”