Course syllabus
LOG211: Model theory, 7.5 credits, Fall 2023
This course is both part of the Master's Programme in Logic as well as available as a free standing course.
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.
This course is divided into two sub-courses:
- 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.
- 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.
Teachers
The course will be taught by Fredrik Engström. You can contact Fredrik by email, fredrik.engstrom@gu.se, or give him a call at +46 - 31 - 786 6335.
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.
Literature
The course is using the book Model Theory for Beginners. 15 Lectures by Roman Kossak. We strongly recommend that you buy this book (it's less than 200 SEK).
Schedule
A schedule is available in TimeEdit. The first lecture is on 29 August 15.15 - 17.00 in room C452.
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.
Course plan (preliminary)
- Week 35: Introduction and preliminaries, chapters 1 and 2.
- Week 36: Definability and symmetry. chapters 3 and 4.
- Week 37: Theories, Types and Elementarity, chapters 5 and 6
- Week 38: Compactness, chapter 7.
- Week 39: Nonstandardness, chapter 8.
- Week 40: Categoricity, chapter 9.
- Week 41: Specialisation
- Week 42: Specialisation
- Week 43: Presentations of the in-depth works.
- Week 44: Deadline for handing in written in-depth work.
More information (recommended exercises, etc) will become available in Modules as the course progresses.
Specialisation
Possible subjects for specialisation:
- Indiscernability and Ehrenfeucht-Mostowski models.
- Skolemization
- Quantifier elimination
- Arithmetic and truth
- Big models and saturation
- Stability (advanced)
- Ehrenfeucht-Fraïssé games
See the module page and the assignment instruction for more info.
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.
Special pedagogical support
If you have a disability and are in need of special pedagogical support please see the information available at the student portal.
Contact information
- Course coordinator Fredrik Engström, fredrik.engstrom@gu.se answers questions about the course content, literature and schedule.
- Education administrator Peter Olsson, peter.olsson.2@gu.se answers questions about registration, examination administration, study interruptions, study breaks, certificates, etc.
- Program Coordinator Rasmus Blanck, rasmus.blanck@gu.se is responsible for programme issues and study guidance for students of the programme.
- Student counselor Peter Olsson, peter.olsson.2@gu.se, is responsible for study guidance of the free-standing course.
Student information
Welcome to the department of Philosophy, Linguistics and Theory of Science
Course summary:
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