Cover; Title; Copyright; 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.
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.