LOG211: Model theory, 7.5 credits, Spring 2022

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. Sometimes, model theory is described as the sum of universal algebra and logic. 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 also brings up two alternative ways to characterise first-order logic, one characterisation uses game theoretic concepts and the other characterise first-order logic in terms of model theoretic properties, Lindström's characterisation.

The course covers central results and concepts in model theory, including:

• Elementary extensions and the Tarski-Vaughts test
• Quantifier elimination
• Compactness and omitting types
• Back-and-forth equivalence and games for elementary equivalence
• ω-categoricity and the random graph
• Saturated models
• Lindström's categorisation of first-order logic

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 based on A shorter model theory by Wilfrid Hodges. Please see the corrigenda for corrections. 

Schedule

Preliminary schedule is available in TimeEdit.

Examination

There will be three obligatory sets of written hand-in problems during the course and at the end of the course there will be a written closed book sit down exam on the course content. 

Course plan (preliminary)

• Week 12: The course starts Thursday March 24. Introduction, chapter 1.
• Week 13: Introduction, chapter 1-2.
• Week 14: Classifying structures, chapter 2.
• Week 15: Structures that look alike, chapter 3.
• Week 16: Compactness, sections 5.1 - 5.3.
• Week 17: The countable case, part I, sections 6.1 - 6.2.
• Week 18: The countable case, part II, sections 6.3 - 6.4.
• Week 19: Saturation, sections 8.1 - 8.2.
• Week 20: Ultraproducts, section 8.5.
• Week 21: Lindström's theorem (Open Logic Textbook).
• Week 22: Written exams. No teaching.

More information (recommended exercises, etc) will be available in Modules. 

Course evaluation

Course report from the last time the course was given can be found Course_report_LOG211_2021-1.pdf here. A summary of the evaluation of this course is also available: Course report LOG211 2022 with Evaluation.pdf 

Learning outcomes

On successful completion of the course the student will be able to:

Knowledge and understanding

• describe and demonstrate an understanding of central concepts, methods and constructions in model theory,
• contrast model theory with other disciplines in logic,
• describe the relationship between the expressive power of logical languages and their ability to characterise structures,

Competence and skills

• formulate and present proofs of the most important results in the course as well as of lemmas that are used in the proofs.

Judgement and approach

• critically discuss, analyse and evaluate results in the course as well as their applications,
• demonstrate the ability to work over disciplinary borders and apply model theoretic results in for example mathematics and computer science.

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 Fredrik Engström, fredrik.engstrom@gu.se is responsible for programme issues and study guidance for students of the programme.
• Student counselor Peter Johnsen, peter.johnsen@gu.se, is responsible for study guidance of the free-standing course.

Student information

Learn Canvas

Checklist for new students

Student Portal

Welcome to the department of Philosophy, Linguistics and Theory of Science

Study Environment and Rules

Plagiarism and academic integrity