**Mathematical Surveys and Monographs**

Volume: 212;
2016;
245 pp;
Hardcover

MSC: Primary 05;

Print ISBN: 978-1-4704-2808-2

Product Code: SURV/212

List Price: $110.00

AMS Member Price: $88.00

MAA Member Price: $99.00

**Electronic ISBN: 978-1-4704-3017-7
Product Code: SURV/212.E**

List Price: $110.00

AMS Member Price: $88.00

MAA Member Price: $99.00

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#### Supplemental Materials

# Ramsey Theory for Product Spaces

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*Pandelis Dodos; Vassilis Kanellopoulos*

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.

I think that this book has a good chance of becoming a classic on density Ramsey theory at the level of the Graham–Rothschild–Spencer book on basic Ramsey theory.

—Stevo Todorcevic, University of Toronto

The book by Dodos and Kanellopoulos is first-rate! It is timely, well written, and has a great selection of topics.

—Ron Graham, University of California, San Diego

#### Readership

Graduate students and researchers interested in Ramsey theory.

#### Table of Contents

# Table of Contents

## Ramsey Theory for Product Spaces

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Chapter 1. Basic concepts 112
- Part 1. Coloring theory 1526
- Chapter 2. Combinatorial spaces 1728
- Chapter 3. Strong subtrees 3748
- Chapter 4. Variable words 5768
- Chapter 5. Finite sets of words 7586
- Part 2. Density theory 8798
- Chapter 6. Szemerédi’s regularity method 89100
- Chapter 7. The removal lemma 109120
- Chapter 8. The density Hales–Jewett theorem 133144
- Chapter 9. The density Carlson–Simpson theorem 155166
- Part 3. Appendices 211222
- Appendix A. Primitive recursive functions 213224
- Appendix B. Ramsey’s theorem 215226
- Appendix C. The Baire property 217228
- Appendix D. Ultrafilters 219230
- Appendix E. Probabilistic background 227238
- Appendix F. Open problems 233244
- Bibliography 237248
- Index 243254
- Back Cover Back Cover1257