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).