Mathematics of Ramsey Theory

Ramsey Theory Old and New.- 1. Ramsey Numbers.- 2. Transfinite Ramsey Theory.- 3. Chromatic Number.- 4. Classical Theorems.- 5. Other Classical Theorems.- 6. Structural Generalizations.- 7. Infinite Ramsey Theorem.- 8. Unprovability Results.- 9. Non-Standard Applications.- I. Classics.- Problems and Results on Graphs and Hypergraphs: Similarities and Differences.- Note on Canonical Partitions.- II. Numbers.- On Size Ramsey Number of Paths, Trees and Circuits. II.- On the Computational Complexity of Ramsey-Type Problems.- Constructive Ramsey Bounds and Intersection Theorems for Sets.- Ordinal Types in Ramsey Theory and Well-Partial-Ordering Theory.- III. Structural Theory.- Partite Construction and Ramsey Space Systems.- Graham-Rothschild Parameter Sets.- Shelah’s Proof of the Hales-Jewett Theorem.- IV. Noncombinatorial Methods.- Partitioning Topological Spaces.- Topological Ramsey Theory.- Ergodic Theory and Configurations in Sets of Positive Density.- V. Variations and Applications.-Topics in Euclidean Ramsey Theory.- On Pisier Type Problems and Results (Combinatorial Applications to Number Theory).- Combinatorial Statements Independent of Arithmetic.- Boolean Complexity and Ramsey Theorems.- Uncrowded Graphs.- Author Index.