This page concerns the course `Model Theory', taught
at the University of Amsterdam from February - May 2019.
This course features in the local
MSc Logic programme
and the national Dutch
Contents of these pages
The 2018/2019 edition of this class has finished.
Next year, the standard 6 EC class Model Theory will be offered in
the Master of Logic programme at the UvA.
- Teaching assistant (homework grading):
- Martijn den Besten, e-mail: martijndenb at gmail dot com
Classes run from 8 February until 24 May.
There are lectures and exercise sessions.
There is one class every week, on Fridays from 10:00 - 12:45 in room SP F1.02
(Science Park, Amsterdam).
- This meeting takes the form of a lecture, but we will also discuss exercises.
- The exam is on 7 June, from 10:00 - 13:00 in room OMHP D1.09
- The resit of the exam is on 28 June, from 10:00 - 13:00 in room
NIKHEF F0.25 (Amsterdam Science Park).
The final grade will be determined by homework assignments and a final exam.
See the special page on grading for more details.
- The main text that we will be using is:
There is additional course material on
- Other pertinent texts are
- Chang, Chen Chung; Keisler, H. Jerome. Model Theory,
Studies in Logic and the Foundations of Mathematics (3rd ed.),
Elsevier, ISBN 978-0-444-88054-3
- Hodges, Wilfrid, A shorter model theory,
Cambridge University Press, 1997,
ISBN-13: 978-0-521-58713-6, ISBN-10: 0521587131
- Marker, David. Model Theory: An Introduction.
Graduate Texts in Mathematics 217. Springer, 2002. ISBN 0-387-98760-6.
- Katrin Tent and Martin Ziegler,
A course in model theory,
Cambridge University Press, 2012,
ISBN-10: 052176324X, ISBN-13: 9780521763240
- Wilfrid Hodges, Model Theory,
Cambridge University Press, ISBN-10: 0521304423, ISBN-13: 978-0521304429
In (first-order) logic, the formal language of mathematical statements and
their interpretation in mathematical structures is carefully identified.
Model theory, then, deals with questions such as:
In this course we will give a general introduction to the methods and results
of classical model theory.
- What classes of structures can be captured by mathematical theories?
- What are the pertinent constructions in mathematics to describe these
- On the other hand, what are the fundamental properties of mathematical
- And, how do these theories relate to properties of the classes of
structures that they describe?
More concretely, we will cover the following topics:
The contents of the final part of the course have not been determined yet,
but will consist of either
- Basic notions: diagrams, compactness, Loewenheim-Skolem Theorem, games
- Classical model theory: ultraproducts, preservation theorems, quantifier elimination
- Types: type spaces, saturation, omitting types, omega-categoricity
an introduction to modern model theory:: (stability: totally transcendental
theories, Morley rank, indiscernibles, Morley's Theorem).
- a special topic such as finite model theory or nonstandard analysis.
We presuppose some background knowledge in formal logic; in particular
familiarity with the syntax and semantics of first-order languages.
basic knowledge of topology will be good, and familiarity with algebraic
structures (such as rings, fields, and vector spaces) 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.
Comments, complaints, questions: mail Yde Venema