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Ramsey theory for product spaces / Pandelis Dodos and Vassilis Kanellopoulos.

By: Contributor(s): Material type: TextTextSeries: Mathematical surveys and monographs ; v 212.Publication details: Providence : American Mathematical Society, ©2016.Description: ix, 245 pages ; 26 cmISBN:
  • 9781470428082
Subject(s): DDC classification:
  • 510MS 23 Am512
Contents:
Chapter 1. Basic concepts -- Part 1. Coloring theory -- Chapter 2. Combinatorial spaces -- Chapter 3. Strong subtrees -- Chapter 4. Variable words -- Chapter 5. Finite sets of words -- Part 2. Density theory -- Chapter 6. Szemerédi's regularity method -- Chapter 7. The removal lemma 120 -- Chapter 8. The density Hales-Jewett theorem -- Chapter 9. The density Carlson-Simpson theorem -- Part 3. Appendices -- Appendix A. Primitive recursive functions -- Appendix B. Ramsey's theorem -- Appendix C. The Baire property -- Appendix D. Ultrafilters -- Appendix E. Probabilistic background -- Appendix F. Open problems.
Summary: Ramsey theory is a dynamic area of combinatorics that has various applications in analysis, ergodic theory, logic, number theory, probability theory, theoretical computer science, and topological dynamics. This book is devoted to one of the most important areas of Ramsey theory--the Ramsey theory of product spaces. It is a culmination of a series of recent breakthroughs by the two authors and their students who were able to lift this theory to the infinite-dimensional case. The book presents many major results and methods in the area, such as Szemerédi's regularity method, the hypergraph removal lemma, and the density Hales-Jewett theorem. This book addresses researchers in combinatorics but also working mathematicians and advanced graduate students who are interested in Ramsey theory. The prerequisites for reading this book are rather minimal: it only requires familiarity, at the graduate level, with probability theory and real analysis. Some familiarity with the basics of Ramsey theory would be beneficial, though not necessary.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510MS Am512 (Browse shelf(Opens below)) Available 137675
Total holds: 0

Includes bibliographical references and index.

Chapter 1. Basic concepts --
Part 1. Coloring theory --
Chapter 2. Combinatorial spaces --
Chapter 3. Strong subtrees --
Chapter 4. Variable words --
Chapter 5. Finite sets of words --
Part 2. Density theory --
Chapter 6. Szemerédi's regularity method --
Chapter 7. The removal lemma 120 --
Chapter 8. The density Hales-Jewett theorem --
Chapter 9. The density Carlson-Simpson theorem --
Part 3. Appendices --
Appendix A. Primitive recursive functions --
Appendix B. Ramsey's theorem --
Appendix C. The Baire property --
Appendix D. Ultrafilters --
Appendix E. Probabilistic background --
Appendix F. Open problems.

Ramsey theory is a dynamic area of combinatorics that has various applications in analysis, ergodic theory, logic, number theory, probability theory, theoretical computer science, and topological dynamics. This book is devoted to one of the most important areas of Ramsey theory--the Ramsey theory of product spaces. It is a culmination of a series of recent breakthroughs by the two authors and their students who were able to lift this theory to the infinite-dimensional case. The book presents many major results and methods in the area, such as Szemerédi's regularity method, the hypergraph removal lemma, and the density Hales-Jewett theorem. This book addresses researchers in combinatorics but also working mathematicians and advanced graduate students who are interested in Ramsey theory. The prerequisites for reading this book are rather minimal: it only requires familiarity, at the graduate level, with probability theory and real analysis. Some familiarity with the basics of Ramsey theory would be beneficial, though not necessary.

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