Francesco Gallinaro's personal webpage

Model Theory

Zeit und Ort Di & Do 12-14 Uhr, Hörsaal II (Albertstr. 23b)
Dozent Dr. Francesco Gallinaro
Sprechstunde Dozent n. V.
E-mail francesco.gallinaro@mathematik.uni-freiburg.de

News

Provisional dates for the oral exams: 20-21-22 February 2024. If these dates are inconvenient for you, please let me know as soon as possible.

Studienleistung/Prüfungsleistung

Please refer to the notes on course and examination achievements in the Modulhanbuch.

For the Studienleistung it will be sufficient to obtain at least 50% of the points available from the exercise sheets. For the Prüfungsleistung it will be necessary to pass an oral examination, to acess which it is necessary to obtain the Studienleistung.

Description

In this course the basics of geometric model theory will be discussed and concepts such as quantifier elimination and categoricity will be introduced. A theory has quantifier elimination if every formula is equivalent to a quantifier-free formula. For the theory of algebraically closed fields of fixed characteristic, this is equivalent to requiring that the projection of a Zariski-constructible set is again Zariski-constructible. A theory is called ℵ1-categorical if all the models of cardinality ℵ1 are isomorphic. A typical example is the theory of non-trivial Q-vector spaces. The goal of the course is to understand the theorems of Baldwin-Lachlan and of Morley to characterize ℵ1-categorical theories.

Literature

Übungsgruppen

The problem sessions (in German) will be delivered by Max Herwig on Thursdays from 4 to 6, in SR 218, Ernst-Zermelo-Str. 1.

Übungsblätter

The exercise sheets (in German) will be released weekly on this webpage.

Sheet Released on To be handed in
Sheet 0 17.10.2023 24.10.2023
Sheet 1 24.10.2023 31.10.2023
Sheet 2 31.10.2023 7.11.2023
Sheet 3 7.11.2023 14.11.2023
Sheet 4 14.11.2023 21.11.2023
Sheet 5 21.11.2023 28.11.2023
Sheet 6 28.11.2023 5.12.2023
Sheet 7 5.12.2023 12.12.2023
Sheet 8 12.12.2023 19.12.2023
Sheet 9 19.12.2023 9.01.2024
Sheet 10 9.01.2024 16.01.2024
Sheet 11 16.01.2024 23.01.2024
Sheet 12 23.01.2024 30.01.2024