Model Theory 2015/2016

This is the website for the Mastermath course ``Model Theory'' which will be offered at the University of Amsterdam in Spring 2016.

Information about the contents of the lectures can be found here.
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: Guillaume Massas
  Email: G.J.Massas@uva.nl
  

Aim

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

Description

In this course we will give a general introduction to the methods and results of model theory. This will include an overview of classical model theory, and an introduction to modern model theory, especially stability theory, leading up to Morley's theorem.

More concretely, the course will be divided into three blocks, covering the following topics:

• Basic notions: diagrams, compactness, Loewenheim-Skolem Theorem, games
• Types: type spaces, saturation, omitting types, omega-categoricity, quantifier-elimination
• Stability: totally transcendental theories, Morley rank, indiscernibles, Morley's Theorem

Practical details

This course is taught as part of the Mastermath programme. This means it is a semester course with one lecture per week (2x45 minutes) followed by an exercise class (60 minutes) starting week 6 and ending week 21. The model theory course is taught on Monday afternoons at the Science Park of the University of Amsterdam. To be precise, the lectures will take place from 14:00 till 15:45 and the exercise classes from 16:00 till 17:00 at Science Park C1.112 (week 6-12) and F1.02 (week 14-21). There will be no lectures or exercise classes on Monday 28 March (Easter) and 16 May (Whitsun).

So first meeting will be on 8 February 14:00 in the lecture hall C1.112 at the Science Park of the University of Amsterdam.

Exam and homeworks

The exam will take place on 6 June from 14:00-17:00 in REC M1.01 (REC = Roeterseilandcampus, Plantage Muidergracht 12), and the resit will take place on 27 June, 14:00-17:00 in Science Park A1.10.

Homework no 4 will be out on 4 April and has to be handed on 11 April, homework no 5 will be out on the 11 April and has to be handed in on 25 April, and homework no 6 will be out on 2 May and has to be handed in on May 11.

Study materials

• Handouts.

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.