## 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
Room: ILLC, Science Park F2.23

Email: martijndenb@gmail.com

## 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

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

- Syllabus available here.

- 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: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.

- 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.

To teaching page.