Screen LibraryIntroduction to ramsey spaces (am-174) /
Ramsey theory is a fast-growing area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. The area of Ramsey theory dealing with Ramsey-type phenomena in higher dimensions is particularly useful. Introduc...
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| Main Authors: | |
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| Corporate Authors: | |
| Published: |
Princeton University Press,
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| Publisher Address: | Princeton, N.J. : |
| Publication Dates: |
[2010] ©2010 |
| Literature type: | eBook |
| Language: | English |
| Edition: | Course Book. |
| Series: |
Annals of mathematics studies;
174 |
| Subjects: | |
| Online Access: |
http://dx.doi.org/10.1515/9781400835409 http://www.degruyter.com/doc/cover/9781400835409.jpg |
| Summary: |
Ramsey theory is a fast-growing area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. The area of Ramsey theory dealing with Ramsey-type phenomena in higher dimensions is particularly useful. Introduction to Ramsey Spaces presents in a systematic way a method for building higher-dimensional Ramsey spaces from basic one-dimensional principles. It is the first book-length treatment of this area of Ramsey theory, and emphasizes applications for related and surrounding fields of mathematics, such as set theory, combinatorics, real and functional analysis, and topology. In order to facilitate accessibility, the book gives the method in its axiomatic form with examples that cover many important parts of Ramsey theory both finite and infinite. An exciting new direction for combinatorics, this book will interest graduate students and researchers working in mathematical subdisciplines requiring the mastery and practice of high-dimensional Ramsey theory. |
| Carrier Form: | 1 online resource (296 pages) : illustrations. |
| ISBN: | 9781400835409 |
| Index Number: | QA166 |
| CLC: | O157.5 |
| Contents: |
Frontmatter -- Contents -- Introduction -- Chapter 1. Ramsey Theory: Preliminaries -- Chapter 2. Semigroup Colorings -- Chapter 3. Trees and Products -- Chapter 4. Abstract Ramsey Theory -- Chapter 5. Topological Ramsey Theory -- Chapter 6. Spaces of Trees -- Chapter 7. Local Ramsey Theory -- Chapter 8. Infinite Products of Finite Sets -- Chapter 9. Parametrized Ramsey Theory -- Appendix -- Bibliography -- Subject Index -- Index of Notation. |