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