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A Guide to NIP Theories
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Details

  • 50 exercises
  • Page extent: 166 pages
  • Size: 228 x 152 mm
  • Weight: 0.4 kg

Library of Congress

  • Dewey number: 511.3/4
  • Dewey version: 23
  • LC Classification: QA9.7 .S536 2015
  • LC Subject headings:
    • Model theory
    • Independence (Mathematics)
    • Logic, Symbolic and mathematical

Library of Congress Record

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Hardback

 (ISBN-13: 9781107057753)

Manufactured on demand: supplied direct from the printer

$120.00 (C)

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.

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; References; Index.

Review

'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

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