Model Theory 2016/2017

This is the website for the course on ``Model Theory'' which will be offered at the University of Amsterdam in February and March 2017.

Exercise sheets, homework sheets and information about grading can be found here.

Teaching staff

• Lecturer: Benno van den Berg
  Email: bennovdberg@gmail.com
  Room: ILLC, Science Park F2.43
• Teaching assistant: Martijn den Besten
  Email: martijndenb@gmail.com
  
Room: ILLC, Science Park F2.23

Aim

The aim of the course is to provide the students with an overview of classical model theory.

Description

In this course we will give a general introduction to the methods and results of classical model theory. More concretely, we will cover the following topics:

• Compactness Theorem
• Lowenheim-Skolem theorems
• Diagrams, Los-Tarski Theorem, Chang-Los-Suszko Theorem
• Ehrenfeucht-Fraisse games
• Directed systems
• Types and type spaces, saturated models
• Countable models: omitting types, omega-categoricity, prime and atomic models
• Quantifier elimination

Practical details

This course is offered in weeks 6 - 12 with an exam in week 13 of 2017. During weeks 6 - 12 there will be two lectures and two exercise class per week. The lectures are on Mondays 13:00-15:00 in SP B0.209 and Wednesdays 13:00-15:00 in SP D1.110. The exercise class are on Tuesdays 9:00-11:00 in SP G0.05 (except for week 7 when it will be in SP D1.111 and week 9 when it will be in G2.02) and Fridays 11:00-13:00 in B0.207.

So the first meeting will be on 6 February 13:00 in the lecture hall B0.209 at the Science Park of the University of Amsterdam.

Exam

The exam will take place on Friday 31 March 9:00-12:00 in SP A1.10. The resit is scheduled for Monday 26 June 15:00-18:00 (location to be determined).

Study materials

• Syllabus available here.

The following texts give an idea of the course's contents:

• Wilfrid Hodges, A shorter model theory, Cambridge University Press, 1997.
• David Marker, Model Theory: an Introduction, Springer Graduate Texts in Mathematics, 2002.
• Katrin Tent and Martin Ziegler, A course in model theory, Lecture Notes in Logic, Cambridge University Press, 2012.

Prerequisites

We presuppose some background knowledge in formal logic; in particular familiarity with the syntax and semantics of first-order languages. Basic knowledge of the following topics will be useful:

• Set theory (Zorn's Lemma, ordinals, cardinals, transfinite recursion)
• Topology (compact space, Hausdorff space, isolated point)
• Algebra (familiarity with rings, fields, and vector spaces): this will be useful in order to be able to appreciate the examples.

More importantly, we assume that participants in the course possess the mathematical maturity as can be expected from students in mathematics or logic at the MSc level.

To teaching page.