Model Theory

6 EC

Semester 2, period 5

5314MOTH6Y

Owner Master Logic
Coordinator A.T. Block Gorman
Part of Master Logic, Master Logic, track Logic and Computation, Master Logic, track Logic and Philosophy, Master Logic, track Logic and Language, Master Logic, track Logic and Mathematics,

Course manual 2025/2026

Course content

In this course we will give a general introduction to the methods and results of classical model theory including games, compactness, the Loewenheim-Skolem theorems, and various preservation theorems, illustrated by examples and applications in algebra and discrete mathematics. Various model theoretic techniques for constructing models will be introduced and applied, such as unions of elementary chains, omitting types construction, ultraproducts and saturated models.

Study materials

Literature

  • Lecture Notes made available on Canvas

Syllabus

  • Will be available on Canvas

Objectives

  • Students will master the use the Compactness Theorem and saturation to construct models with specific types of phenomena.
  • Students will learn to eliminate quantifiers both syntactically and semantically.
  • Students will learn to construct models with various other desirable properties, such as unions of elementary chains, omitted types, ultraproducts/ultrapowers, etc.
  • Students will gain competence in axiomatizing the first order theory of certain basic mathematical structures. Students will furthermore master techniques for showing that the axiomatizations in question are complete.

Teaching methods

  • Lecture
  • Seminar
  • Self-study

Weekly lectures are used to present the material, while weekly exercise sessions are used for students to practice and receive individual feedback. Six homework assignments are submitted in pairs, with feedback provided to the students in online comments, and solutions are also made available. Two quizzes will be given during a couple of the lectures.

Learning activities

Activity

Number of hours

Zelfstudie

168

Attendance

This programme does not have requirements concerning attendance (TER-B).

Additional requirements for this course:

This programme does not have requirements concerning attendance (TER-B).

Assessment

Item and weight Details

Final grade

1 (100%)

Tentamen

The final exam counts for 65% of the final grade, there will be two quizzes that count for 10% of the final grade, and homework submissions count for 25%. Exams are written on paper and graded manually. Missed assignments and quizzes are graded as 0%, unless there are exceptional circumstances. Solutions for the homework assignments and quizzes will be posted on Canvas.

Inspection of assessed work

The homework and quiz feedback is visible to the students digitally on Canvas. For the final exam, students have the opportunity to view their work and how the rubric was applied.

Assignments

This course will include six weekly assignments.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Weeknummer Onderwerpen Studiestof
1
2
3
4
5
6
7
8

Additional information

We presuppose some (but very little) background knowledge in logic; roughly, what is needed is familiarity with the syntax and semantics of first-order languages. More importantly, we assume that participants in the course possess some mathematical maturity, as can be expected from students in mathematics or logic at a MSc level.

Contact information

Coordinator

  • A.T. Block Gorman