LOG210: Model theory, 7.5 credits, Spring 2020

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.

Literature

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

Schedule

Will be published closer to the start of the course.

Course plan

Please see the Modules page for the course plan.

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.