Model Theory
This page concerns the course `Model Theory', taught
at the University of Amsterdam from February - May 2012.
This course features in the
local MSc Logic programme.
Contents of these pages
- Note that the location of the exam has changed --
the correct location is given below.
- Material to be covered on May 23: Lindström's Theorem.
Here are Jouko Väänänen's slides
on the topic, and here are some
exercises.
-
Here is last year's exam.
(Note that saturation was not covered last year.)
-
The sixth homework assignment is available.
Deadline for handing this in will be Wednesday, May 23.
Staff
- Lecturer:
- Teaching assistants:
- Shenyang Zhong, e-mail zhongshengyang at 163.com
-
Zhenhao Li, e-mail zhenhaolee at gmail.com
Dates/location:
-
Classes run from September 6 until May 23; there will be 14/15 class weeks
in total.
-
Lectures are on Wednesdays from 15.00 - 17.00:
- February 8,15: room A1.10
- February 22, 29, March 7,14,21: room B0.201
- April, May: D1.115
-
Tutorial sessions are on Thursdays from 09.00 - 11.00:
- February 9,16: room G0.05
- February 23, March 1,8,15,22: room B0.201
- April, May: D1.115
- The exam is on May 31, from 13.00 - 16.00 in room D1.115 (and possibly
D1.116)..
- All of these rooms are in the Science Park.
-
Here
is a map of the Amsterdam Science Park area.
-
The final grade will be determined by homework assignments and a final exam.
More details to follow.
Course material
- The main text that we will be using is:
- Hodges, Wilfrid, A shorter model theory,
Cambridge University Press, 1997,
ISBN-13: 978-0-521-58713-6, ISBN-10: 0521587131
Corrigenda to the book.
- Of this book, we will cover most of the chapters 1, 2, 3, 5, 6, and
section 8.5.
- 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
- Wilfrid Hodges, Model Theory,
Cambridge University Press, ISBN-10: 0521304423, ISBN-13: 978-0521304429
- Marker, David (2002). Model Theory: An Introduction.
Graduate Texts in Mathematics 217. Springer. ISBN 0-387-98760-6.
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:
-
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 they relate to properties of the classes of structures that they
describe?
These questions are fundamental to the whole enterprise of mathematics and the
insights and methods of model theory have far-reaching consequences in many
branches of mathematics.
For a nice introduction and overview of the field, please see the
Stanford Encyclopedia
of Philosophy.
In this course we will give a general introduction to the methods and results of
classical model theory including compactness, the Löwenheim-Skolem theorems, and
various preservation theorems illustrated by examples and applications in
algebra, analysis, and discrete mathematics.
Various model theoretic techniques
for constructing models will be introduced and applied, such as unions of
elementary chains, omitting types construction, ultraproducts and saturated
models.
Prerequisites
We presuppose some (but very little) background knowledge in logic;
roughly, what is needed is familiarity with the syntax and semantics of
first-order languages.
More importantly, we assume that participants in the course possess some
mathematical maturity as can be expected from students in mathematics or logic
at a MSc level.
Comments, complaints, questions: mail Yde Venema