General Information
Time and Place: MWF
1111:50am,
300
Lincoln Hall
Control Number: 06882
Instructor:
Matthias
Aschenbrenner
Email address:
Homepage: http://www.math.uic.edu/~maschenb
Office: 616
SEO
Office Phone: (312) 4132163
Office Hours: MWF 1011am,
or by appointment.
Prerequisites:
Graduate standing and familiarity with basic
concepts of mathematical logic, e.g., structures, sentences,
formulas,
satisfaction, theories.
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Description
An
introduction to model theory, emphasizing both general theory and
applications
to algebra. Specific topics to be covered include:

Review of basic notions (like
languages,
structures etc.), and the Compactness Theorem

Quantifier elimination and the
model
theory of the real and complex fields (and more algebraic examples,
perhaps)

Saturated and homogeneous models

Omitting types and prime models

Indiscernibles, perhaps leading
to a
proof of Morley's Theorem (if time permits)
Course Text
I
will mostly (but not exclusively) follow Model
Theory: An Introduction by David
Marker, SpringerVerlag, 2000.
Other
texts on model theory that you might want to consult:

A Course
in Model Theory:
An Introduction to Contemporary Mathematical Logic
by Bruno Poizat, SpringerVerlag, 2000. (A Russian copy of
Poizat's
book may be downloaded
and you can write (en français) to the author
to buy a copy of the book in French.)

A Shorter Model Theory
by Wilfrid Hodges,
Cambridge University Press, 1997. (See corrigenda.)
An expanded version of this book is available under the title
Model Theory.

Introduction to Model
Theory
by Philipp
Rothmaler, Gordon and Breach Science Publishers, 2000.

Model Theory by C.
C.
Chang and H. J. Keisler,
NorthHolland, 1998.

If you feel adventurous, check
out the
lecture
notes (in German!) for a course in model theory taught by Volker
Weispfenning which I wrote a long time ago.
A good general reference for
mathematical
logic is Mathematical
Logic
by
Joseph
R. Shoenfield, A K Peters, Ltd., 2000.
The classical works of Abraham
Robinson, Introduction
to Model Theory and the Metamathematics of Algebra (1963), Complete
Theories, (1956; new edition 1976), and On
the Metamathematics of Algebra (1951) are still worth reading.
For a collection of recent survey
articles on model theory see here.
Homeworks
There will be a problem set due
every
two weeks or so, to be handed in at the beginning of class. Up to 3
individuals
may work together on homework problems (and I encourage you to do so),
but when you turn in the problem set you should acknowledge that you
have
collaborated.
Problem Set
1 (due February 6). For solutions click here.
Problem Set
2 (due February 20). For solutions click here.
Problem Set
3 (due March 5). For solutions click here.
Problem Set
4 (due March 29). For solutions click here.
Problem Set
5 (due April 16). For solutions click here.
Problem Set
6 (due April 30). For solutions click here.
Historical Information
Click
below for biographical information about some prominent model theorists:
Kurt
Gödel
Leopold
Löwenheim
Anatoly
Ivanovich Malcev
Andrzej
Mostowski
Abraham
Robinson
Thoralf
Skolem
Alfred
Tarski
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Last
modified 05/10/04.