Model theory
Lecture of the module MA Ba-ALGSTR "Algebraische Strukturen: Diskrete Strukturen", Summer Semester 2021. Subtitle: Model Theory
News
- Because of the Corona Pandemie, there will be no physical meetings until further notice. However, the course will start ONLINE at the regular date.
- IMPORTANT: please send me an email if you are interested in participating so that I can reach you. Details about how we proceed with the course will be communicated by email.
- Please also register in Opal. REGISTRATION NOW ACTIVE.
Language
English on demand. Please send me an email if you are interested in this course and would like the language of the course to be English.
Topics
- Elementary extensions and substructures
- Compactness via ultraproducts
- The theorem of Löwenheim-Skolem
- Amalgamation classes and homogeneous structures
- Realising and omitting types
- Countable Categoricity
- Model Completeness and Quantifier Elimination
- Example: Algebraically Closed Fields, real closed fields (if time permits)
- Stability, the independence property, the strict order property
Target audience
Bachelor mathematics; Diploma computer science students with a minor in mathematics
Prerequisites
You should bring the skills that are taught e.g. in the Modules Math-Ba-ANAG, Math-Ba-LAAG and Math-Ba-PROG. Knowledge of the material from "Introduction to Mathematical Logic" is certainly useful. For the computer science students: You should bring the skills from the obligatory math courses for computer scientists at TU Dresden, and you should know first-order logic (which is taught in computer science courses).
Times
| Tuesday | 3. DS |
Online |
| Friday | 3. DS | Online |
Literature
The lecture does not strictly follow a book, but rather the course notes. But there are many excellent text books about model theory, for example:
- 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.
Course Notes
The basis for the course are the (english) course notes (some chapters are still in preparation).