Course syllabus

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LOG211: Model theory, 7.5 credits, Spring 2021

This course is both part of the Master's Programme in Logic as well as available as a free standing course. 

The course starts with detailed proofs of compactness and omitting types for first-order logic. Students is then introduced to a number of central methods, constructions and results with a focus on model completeness, automorphism groups and omega categoricity, ultraproducts, o-minimality, interpretability and back-and-forth equivalence.

Quantifier elimination and zero-one laws serve as an introduction to applications of model theory to computer science. The course also deals with Morley's theorem and the basics of stability theory.

TeachersPhoto of Fredrik Engström

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

The schedule is available in TimeEdit:
https://cloud.timeedit.net/gu/web/schema/ri1X7086Z11092QQ58Z64YuY0Zy95Y57QQXwXY622v56l974Qx690492919698X64587YY652.html#

All lectures are done over zoom, using this link:
https://gu-se.zoom.us/j/61296356655?pwd=M1c2OWpjdElWTVpxRHkrT0hLNU1NQT09  

Examination

There will be three sets of written hand-in problems during the course. These will be assessed with the grades U, G, or VG. If you get a U there will be a possibility for you to hand-in new solutions to get a G.

At the end of the course, when all three hand-in sets has been passed, there will be a short oral examination on the course content. This will be done over video link och you will need to identify yourself with an ID-card. The oral exam is assessed with U or G.

For passing the course you will need to pass all four examination steps (i.e., get a G). To get a VG on the course you will need to pass the oral exam and get VG on all the hand-in assignments.

Course plan

  • Week 13: The course starts Thursday March 26. Introduction, chapter 1.
  • 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: Oral exams. No teaching.

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

Course evaluation

Course report can be found here.

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 Linda Aronsson, linda.aronsson@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 

Course summary:

Date Details Due