The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.
Special thanks to Matěj Konečný for helpful feedback.
Title: Bootcamp 4 (of 8)
Lecturer: Jaroslav Nešetřil
Date: Monday September 26, 2016.
Main Topics: Graphs have the ordering property, Ordered Edge-Ramsey implies Ordering property, Graphs are not Ramsey, Amalgamation for Ramsey classes, the product argument, Hilbert’s Theorem.
Definitions: Joint Embedding Property, Amalgamation Property, statement of Hilbert’s Theorem.