## Dual Ramsey, an introduction – 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: Dual Ramsey, the Gurarij space and the Poulsen simplex 1 (of 3).

Lecturer: Dana Bartošová.

Date: December 12, 2016.

Main Topics: Comparison of various Fraïssé settings, metric Fraïssé definitions and properties, KPT of metric structures, Thick sets

Definitions: continuous logic, metric Fraïssé properties, NAP (near amalgamation property), PP (Polish Property), ARP (Approximate Ramsey Property), Thick, Thick partition regular.

Lecture 1 – Lecture 2 – Lecture 3

Ramsey DocCourse Prague 2016 Index of lectures.

## Introduction to the KPT correspondence 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: Introduction to the KPT correspondence 3 (of 3).

Lecturer: Lionel Ngyuen Van Thé.

Date: November 18, 2016.

Main Topics:

Definitions: Expansion property,

Lecture 1Lecture 2 – Lecture 3

## Introduction to the KPT Correspondence 2 – 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: Introduction to the KPT correspondence 2 (of 3).

Lecturer: Lionel Ngyuen Van Thé.

Date: November 16, 2016.

Main Topics: Computing universal minimal flows, $M(S_\infty)$, why precompactness is important.

Definitions: Minimal flow, universal flow, Logic action, $G$-equivariant.

Lecture 1 – Lecture 2 – Lecture 3

## Topological dynamics and Ramsey classes – 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: Topological dynamics and Ramsey classes.

Lecturer: Lionel Ngyuen Van Thé.

Date: November 14, 2016.

Main Topics: Proof of KPT correspondence between extreme amenability and ramsey class.

Definitions: Topological group, $S_\infty$, $d_R, d_L$, Polish group, ultrametric, $G$-flow, extreme amenability.

## Bootcamp 5 – 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 5 (of 8)

Lecturer: Jan Hubička

Date: Friday September 30, 2016.

Main Topics: Rado Graph, Fraïssé’s Theorem, Examples of Fraïssé classes, Ramsey implies Amalgamation, Lifts and Reducts, Ramsey classes have linear orders

Definitions: Extension Property, Ultrahomogeneous, Universal, $\text{Age}(A)$, Fraïssé class, irreducible structure, Lifts/Expansions and Shadows/reducts.

Bootcamp 1 – Bootcamp 2 – Bootcamp 3Bootcamp 4 – Bootcamp 5 – Bootcamp 6Bootcamp 7 – Bootcamp 8