# Bootcamp 2 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes were taken and edited by myself and Michael Kompatscher. In the process we may have included some errors; email us or comment below and we will happily fix them.

Title: Bootcamp 2 (of 8)

Lecturer: Jaroslav Nešetřil.

Date: September 21, 2016.

Main Topics: The Rado graph, homogeneous structures, universal graphs

Definitions: Language, structures, homomorphisms, embeddings, homogeneity, universality, Rado graph (Random graph),…

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

## Introduction

In this lecture we discussed some standard notions from model theory that will be used in the rest of the Bootcamp lectures. Further we discussed the Rado graph (also known as Random graph) as an example of a homogeneous structure.

## Structures

Definition. A language (or signature) $L$ is a set of symbols, which can be diveded into relational symbols (usually denoted by capital letters $R$) and functional symbols (usually described by lowercase letters $f$). To every symbol $R$ we associate an natural number $\text{ar}(R)$, the arity of $R$.

## References

1. Peter Cameron, The Random graph, 2013.
2. Dugald MacPherson, A survey of homogeneous structures, 2011.
This entry was posted in Course Notes, Ramsey DocCourse Prague 2016. Bookmark the permalink. Both comments and trackbacks are currently closed.