Course syllabus

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LOG211: Model theory, 7.5 credits, Fall 2025

This course is both part of the Master's Programme in Logic as well as available as a free standing course.  The course will be taught by Ivan Di Liberti. The examiner is Fredrik Engström. The schedule is available on TimeEdit.

Course content

Model theory is the study of first-order structures on the basis of the relationship with logical languages. Questions that are studied concern, among other things, the expressive power of logical languages in terms of the ability to classify structures, and what sort of models can be constructed. The course covers basic concepts and results in model theory, and also let the student specialise in a well delimited field of model theory.

Short Syllabus. First order languages. Theories and their models. Loweinheim-Skolem theorems. Ultraproducts and compactsness. Model-completeness and quantifier elimination. Types. Saturated models. Prime models and a glance into categoricity. 

Literature and study material.

Structure of the course

This course is divided into two sub-courses:

  1. The basics of model theory, 4.5 credits. The sub-course treats basic and key concepts and results in model theory, including: definability, homomorphisms, elementary extensions, compactness and categoricity.
  2. Specialisation within model theory, 3 credits. The sub-course entails an in-depth study in an area of model theory or an application of a model-theoretic method in a neighboring area. The in-depth subject must be chosen in consultation with the course coordinator.

The first sub-course will be taught frontally, for a total of approximately 12 lectures. The second sub-course comprises a project. Students will be assigned a topic to work on independently. Every student will have to create a document of 3 to 5 pages presenting the topic, stressing on its relevance in the scientific landscape in which it emerged. This includes: the main problems that originated the subjects, its initial historical developments, its main techniques, its main results, a list of the main contributors, papers, books (or surveys) and an extensive list of references. The suggested literature for the projects below can be found here.

Examination

The course is examined individually in written form. In addition to a written exam on the first part of the course, the second part of the course is examined through an individual written in-depth work. The written exam will be a closed book sit down exam on the course content.

The dates for the exam have been fixed:

  • Main exam: On the 14th October 08:00-12:00 at Andra Långgatan 19.
  • Retake: On the 18th November, 13:00-17:00 at Första Långgatan 16.

Register for the course

You will be able to register for the course one week before it starts. When you have registered for the course you will get access to more course information. You can find information regarding registration here.

Course evaluation

Course report from the last time the course was given can be found here: Course report LOG211 2022 with Evaluation.pdf 

Learning outcomes

See the course syllabus for more information. 

Contact information

  • Course coordinator Ivan Di Liberti,  ivan.di.liberti@gu.se answers questions about the course content, literature and schedule.
  • Education administrator Sandra Schriefer, sandra.schriefer@gu.se  answers questions about registration, study interruptions, study breaks, certificates, etc. 
  • Education administrator about Annika Herrström, annika.herrstrom@gu.se  answers questions about examination administration.
  • Program Coordinator Ivan Di Liberti,  ivan.di.liberti@gu.se is responsible for programme issues and study guidance for students of the programme.
  • Education Coordinator Andreas Ott, andreas.ott@gu.se 
  • If you have a disability and are in need of special pedagogical support please see the information available at the student portal. 

Course summary:

Course Summary
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