Ramsey Theory of Homogeneous Structures

Ramsey Theory of Homogeneous Structures

International Mathematical Union via YouTube Direct link

Intro

1 of 27

1 of 27

Intro

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Ramsey Theory of Homogeneous Structures

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  1. 1 Intro
  2. 2 Pigeonhole Principle
  3. 3 Ramsey's Theorems, 1930
  4. 4 The Rationals as a Dense Linear Order
  5. 5 Coloring Finite Sets of Rationals
  6. 6 Example: Colorings of copies of a finite graph
  7. 7 Homogeneous and Universal Structures
  8. 8 Infinite Structural Ramsey Theory
  9. 9 Big Ramsey Degree results up to 2010
  10. 10 Methodology for red highlighted results
  11. 11 Milliken's Theorem (special case)
  12. 12 Diagonal Antichains
  13. 13 Exact Big Ramsey Degrees of the Rado graph
  14. 14 Prior Methods Insufficient for Triangle-Free Graphs
  15. 15 New developments: how forcing opened new paths
  16. 16 Diagonal Coding Tree T within Coding Tree of 1-types
  17. 17 Forcing a Level Set Pigeonhole
  18. 18 Exact Big Ramsey Degrees for H3
  19. 19 Precise characterization of big Ramsey degrees for Hz
  20. 20 T(Edge, H3) = 2
  21. 21 T(Non-Edge, H3) = 5
  22. 22 Developments via coding trees and forcing
  23. 23 Developments not using forcing
  24. 24 Upper Bounds for Binary Free Amalgamation Classes
  25. 25 Exact Big Ramsey Degrees for binary free amalgamation
  26. 26 Big Question
  27. 27 Ongoing Investigations

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