Zeit und Ort | Di & Do 12-14 Uhr, Hörsaal II (Albertstr. 23b) |

Dozent | Dr. Francesco Gallinaro |

Sprechstunde Dozent | n. V. |

francesco.gallinaro@mathematik.uni-freiburg.de |

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.

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.

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 ℵ_{1}-categorical if all the models of cardinality ℵ_{1} 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 ℵ_{1}-categorical theories.

- B. Poizat: A Course in Model Theory, Springer, 2000. Available online.
- K. Tent, M. Ziegler: A Course in Model Theory, Cambridge University Press, 2012.
- M. Ziegler: Vorlesung über Modelltheorie, online notes.

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

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 |