Model Theory
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
Mastermath programme.
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.
Staff
 Lecturer:
 Teaching assistant (homework grading):
 Martijn den Besten, email: martijndenb at gmail dot com
Dates/location:

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
(Amsterdam Center).
 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.
Course material
 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 9780444880543
 Hodges, Wilfrid, A shorter model theory,
Cambridge University Press, 1997,
ISBN13: 9780521587136, ISBN10: 0521587131
 Marker, David. Model Theory: An Introduction.
Graduate Texts in Mathematics 217. Springer, 2002. ISBN 0387987606.
 Katrin Tent and Martin Ziegler,
A course in model theory,
Cambridge University Press, 2012,
ISBN10: 052176324X, ISBN13: 9780521763240
 Wilfrid Hodges, Model Theory,
Cambridge University Press, ISBN10: 0521304423, ISBN13: 9780521304429
In (firstorder) logic, the formal language of mathematical statements and
their interpretation in mathematical structures is carefully identified.
Model theory, then, deals with questions such as:
 What classes of structures can be captured by mathematical theories?
 What are the pertinent constructions in mathematics to describe these
classes?
 On the other hand, what are the fundamental properties of mathematical
theories?
 And, how do these theories relate to properties of the classes of
structures that they describe?
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:
 Basic notions: diagrams, compactness, LoewenheimSkolem Theorem, games
 Classical model theory: ultraproducts, preservation theorems, quantifier elimination
 Types: type spaces, saturation, omitting types, omegacategoricity
The contents of the final part of the course have not been determined yet,
but will consist of either

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.
Prerequisites
We presuppose some background knowledge in formal logic; in particular
familiarity with the syntax and semantics of firstorder languages.
Some
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