Introduction to Ramsey Spaces (AM-174)

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Princeton University Press, Jul 1, 2010 - Mathematics - 296 pages
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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.

 

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Contents

Introduction
1
Preliminaries
3
Chapter 2 Semigroup Colorings
27
Chapter 3 Trees and Products
49
Chapter 4 Abstract Ramsey Theory
63
Chapter 5 Topological Ramsey Theory
93
Chapter 6 Spaces of Trees
135
Chapter 7 Local Ramsey Theory
179
Chapter 8 Infinite Products of Finite Sets
219
Chapter 9 Parametrized Ramsey Theory
237
Appendix
259
Bibliography
271
Subject Index
279
Index of Notation
285
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About the author (2010)

Stevo Todorcevic is professor of mathematics at the University of Toronto and holds senior research positions at the CNRS in Paris and SANU in Belgrade. He is the author or coauthor of several books, including "Walks on Ordinals and Their Characteristics" and "Ramsey Methods in Analysis".

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