Model theory summer semester 2025/26
Lecture of the module Math-Ma-02, winter semester 2025/26.
Subtitle: Model theory
Language
TBA
Topics
- Elementary extensions and substructures
- The compactness theorem using ultra products
- The Löwenheim and Skolem theorem
- Amalgamation classes and homogeneous structures
- Type realisation and type avoidance
- Countable categorical structures
- Model completeness and quantum elimination
- Example: Algebraically closed solids, real closed solids
- Stability, independence property, strict order property
Target groups
Master's degree in Mathematics, Computer Scientists
Previous knowledge
Math-Ba-LA10, Math-Ba-LA20
Lecture times
TBA
Literature
The lecture does not follow a textbook, but the script. However, there are many excellent textbooks for model theory, e.g.
- "A Shorter Model Theory" (Cambridge University Press) by Wilfrid Hodges, 1997.
- "A Course in Model Theory" (Cambridge University Press) by Katrin Tent and Martin Ziegler, 2012.
Script
The basis for the selection of topics is the script (some chapters will follow shortly).