Chapter 18. Multidimensional Ramsey Theory

Chapters in this book

1. Frontmatter i
2. Preface to the First Edition v
3. Preface to the Second Edition ix
4. Notation xi
5. Contents xiii
6. Part I. Background Development
7. Chapter 1. Semigroups and Their Ideals 3
8. Chapter 2. Right Topological (and Semitopological and Topological) Semigroups 38
9. Chapter 3. ßD-Ultrafilters and The Stone– Čech Compactification of a Discrete Space 56
10. Chapter 4. ßS – The Stone–Čech Compactification of a Discrete Semigroup 85
11. Chapter 5. ßS and Ramsey Theory – Some Easy Applications 108
12. Part II. Algebra of ßS
13. Chapter 6. Ideals and Commutativity in ßS 127
14. Chapter 7. Groups in ßS 168
15. Chapter 8. Cancellation 196
16. Chapter 9. Idempotents 226
17. Chapter 10. Homomorphisms 252
18. Chapter 11. The Rudin–Keisler Order 271
19. Chapter 12. Ultrafilters Generated by Finite Sums 286
20. Chapter 13. Multiple Structures in ßS 308
21. Part III Combinatorial Applications
22. Chapter 14. The Central Sets Theorem 331
23. Chapter 15. Partition Regularity of Matrices 364
24. Chapter 16. IP, IP*, Central, and Central* Sets 405
25. Chapter 17. Sums and Products 427
26. Chapter 18. Multidimensional Ramsey Theory 460
27. Part IV. ConnectionsWith Other Structures
28. Chapter 19. Relations With Topological Dynamics 491
29. Chapter 20. Density – Connections with Ergodic Theory 508
30. Chapter 21. Other Semigroup Compactifications 523
31. Bibliography 555
32. Index 577