Bootcamp 6 – Ramsey DocCourse Prague 2016

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.

Title: Bootcamp (6 of 6)

Lecturer: Jaroslav Nesetril

Date: Monday October 3, 2016.

Main Topics: Other applications of the “product argument”, Chain-Ramsey for Posets, Proof of edge-Ramsey for Graphs, Proof of Hales-Jewett

Definitions: Structural pigeonhole principle, Poset, Graph product, Combinatorial line

Bootcamp 1 – Bootcamp 2 – Bootcamp 3Bootcamp 4Bootcamp 5 – Bootcamp 6
Continue reading Bootcamp 6 – Ramsey DocCourse Prague 2016

Bootcamp 3 – Ramsey DocCourse Prague 2016

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.

Title: Bootcamp (3 of 6)

Lecturer: Jaroslav Nešetřil

Date: Friday September 23, 2016.

Main Topics: Point Ramsey for graphs, \langle A,B,C \rangle hypergraphs.

Definitions: Ramsey property for finite structures, Ramsey Class, point-Ramsey, edge-Ramsey, \langle A,B,C \rangle hypergraphs, Chromatic number, Ordering Property.

Bootcamp 1 – Bootcamp 2 – Bootcamp 3 – Bootcamp 4Bootcamp 5Bootcamp 6 – Bootcamp 7

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Van der Waerden’s Theorem is false for $latex \omega_1 $

One of my main research problems involves something I think is related to arithmetic progressions in \mathbb{Z} . After learning a nice proof of Van der Waerden’s Theorem, and sharing it with colleagues, Daniel Soukup asked a nice question about Van der Waerden’s Theorem on \omega_1 . We answered it, and the example was sufficiently nice that I would like to share it.

Continue reading Van der Waerden’s Theorem is false for \omega_1 

Van der Waerden’s Theorem is false for $latex omega_1 $

One of my main research problems involves something I think is related to arithmetic progressions in mathbb{Z} . After learning a nice proof of Van der Waerden’s Theorem, and sharing it with colleagues, Daniel Soukup asked a nice question about Van der Waerden’s Theorem on omega_1 . We answered it, and the example was sufficiently nice that I would like to share it.

Continue reading Van der Waerden’s Theorem is false for omega_1