Model theory summer semester 2025/26

Lecture of the module Math-Ma-02, winter semester 2025/26.
Subtitle: Model theory

Language

English.

Course Description

This course introduces the fundamentals of modern model theory. Topics include elementary substructures and extensions, compactness via ultraproducts, the Löwenheim–Skolem theorem, amalgamation classes and homogeneous structures, types and omitting types, countably categorical structures, model completeness and quantifier elimination, algebraically and real closed fields, as well as stability, the independence property, and the strict order property.

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 and places

• Mondays 2nd time slot (9h20), room Wil C104.  

• Tuesdays 2nd time slot (9h20), room Wil C106.

Internal Area

Please subscribe in Opal

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).