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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...
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| Main Authors: | |
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| Group Author: | |
| Published: |
American Mathematical Society,
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| Publisher Address: | Providence, Rhode Island : |
| Publication Dates: | [2016] |
| Literature type: | Book |
| Language: | English |
| Series: |
Mathematical surveys and monographs ;
volume 212 |
| Subjects: | |
| 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. |
| Carrier Form: | ix, 245 pages ; 26 cm. |
| Bibliography: | Includes bibliographical references (pages 237-241) and index. |
| ISBN: |
9781470428082 (hardback : alkaline paper) : 1470428083 (hardback : alkaline paper) |
| Index Number: | QA164 |
| CLC: |
O189.11 O157.1 |
| Call Number: | O157.1/D646 |
| 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. |