General Information
Time and Place: MWF
11-11:50am,
300
Lincoln Hall
Control Number: 06882
Instructor:
Matthias
Aschenbrenner
E-mail address: 
Homepage: http://www.math.uic.edu/~maschenb
Office: 616
SEO
Office Phone: (312) 413-2163
Office Hours: MWF 10-11am,
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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to download the class information handout.
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, Springer-Verlag, 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, Springer-Verlag, 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,
North-Holland, 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.
