| Zeit und Ort | Mo & Mi 14-16 Uhr, SR 127 (Ernst-Zermelo-Str. 1) |
| Dozent: | Prof. Dr. Amador Martin-Pizarro |
| Sprechstunde Dozent: | n. V. |
| Assistenz: | Charlotte Amann-Bartnick |
| Sprechstunde Assistentin: | TBA, Raum 305 |
| E-Mail Anfragen: | charlotte[punkt]bartnick[at]math[punkt]uni-freiburg[punkt]de |
The lectures and the problem session will be held in English. The problem sheet can be handed in either in English or in German.
The problem session will take place on Tuesdays from 4 - 6 pm in room 318. The exercise sheets will be posted on this website on Monday evening or Tuesday morning and must be handed in approximately a week later by Monday 10 am in the (yellow) mailbox 3.19 in the basement of the Mathematical Institute (Ernst-Zermelo-Str. 1).
Please refer to the Modulhandbuch for the conditions on the Studien- and Prüfungsleistung.
For the Studienleistung it will be sufficient to obtain at least 50% of the points available from the exercise sheets
The proof of Baldwin and Lachlan of Morley's theorem introduces the notion of $\omega$-stability, which lies in the core of many applications of model theory to algebraic geometry and number theory. In this lecture we will introduce Morley rank, a meaningful dimension in $\omega$-stable theories, and prove, among others, Macintyre's theorem, which states that an infinite $\omega$-stable field must be algebraically closed. Similarly, we will prove Reineke's theorem, which states that a connected $\omega$-stable group of rank 1 is abelian. In order to give a full proof of these two theorems, we need to introduce the notions of generic types in $\omega$-stable groups as well as imaginaries.
The sheets have to be handed in till 10:00 am at the indicated dates below.
| Sheet | Released on | To be handed in |
| Sheet 0 | 22.04.26 | not to be handed in |
| Sheet 1 | 27.04.26 | 04.05.26 |
| Sheet 2 | 04.05.26 | 11.05.26 |
| Sheet 3 | 12.05.26 | 18.05.26 |
| Sheet 4 | 18.05.26 | 01.06.26 |
| Sheet 5 | 01.06.26 (! corrected version from 03.06.) | 08.06.26 |
| Sheet 6 | 08.06.26 | 15.06.26 |
| Sheet 7 | 15.06.26 | 22.06.26 |
The following literature is recommended:
