# Christian d'Elbée

## Teaching page

### Neostability and independence relations

This concerns the course:

- V5A7 - Advanced Topics in Mathematical Logic (SoSe 2022-23) Neostability and Independence relations.

The lectures are given as follows:
- Tuesday: 14:00 (c.t.)-- 16:00 Wegelerstr. 10 - Kleiner Hörsaal
- Wednesday 12:00 (c.t.) -- 14:00 Endenicher Allee 60 - SemR 0.006

The starting date is Tuesday 04 april, 2023. The last course will be given on the 5th of July, 2023.
Here is the link to Basis.
#### Office Hours

I will be in my office (4.004 in the Mathematisches Institute) for answering questions every Tuesday between 16:00 and 17:00.
#### Abstract

The course will introduce the fruitful links between model theory and a combinatoric of sets given by axiomatic independence relations. One of the main goals of this course is to get familiar with the so-called "forking calculus", which consists of a model-theoretic abstraction of arguments from elementary algebraic geometry and field theory to a general level. We will cover the Kim-Pillay theorem (the characterisation of simple theories by the presence of a well-behaved independence relation), the Harnik-Harrington principle (similar but for stable theories), and few steps into the wider classes of NSOP1 and NSOP4 theories. We will also cover some results purely about axiomatic theory of independence, such as Adler's "theorem of symmetry". We will illustrate the abstract results by concrete examples which we will study all along the course: algebraically closed fields, generic predicate/functions on a field, random graphs, pseudo-finite fields.
#### Prerequisites

Basic level in model theory. Participation in the course
Advanced Mathematical Logic during the SoSe 2021/22 is helpful and recomended, but not compulsory. You can find the notes of the latter course here . Participation in the course Advanced Mathematical Logic II (V4A8) WiSe 2022/23 will not be especially helpful, since arguments will be of different nature. The complete list of notions I will assume known is the following: languages, sentences, theories, formulas, types, structures, definable sets, substructures, elementary substructures, models, elementary maps, elementary bijections and automorphism of models. I recommend Tent and Ziegler "A course in Model Theory" for those notions.
#### Content

The notes of the course are available below.