Time and Place: MWF
Control Number: 06882
Office Phone: (312) 413-2163
Office Hours: MWF 10-11am,
or by appointment.
Graduate standing and familiarity with basic
concepts of mathematical logic, e.g., structures, sentences,
files from this website requires software to display PDF files, such as
Reader or Ghostview.
to download the class information handout.
introduction to model theory, emphasizing both general theory and
to algebra. Specific topics to be covered include:
Review of basic notions (like
structures etc.), and the Compactness Theorem
Quantifier elimination and the
theory of the real and complex fields (and more algebraic examples,
Saturated and homogeneous models
Omitting types and prime models
Indiscernibles, perhaps leading
proof of Morley's Theorem (if time permits)
will mostly (but not exclusively) follow Model
Theory: An Introduction by David
Marker, Springer-Verlag, 2000.
texts on model theory that you might want to consult:
A good general reference for
logic is Mathematical
R. Shoenfield, A K Peters, Ltd., 2000.
in Model Theory:
An Introduction to Contemporary Mathematical Logic
by Bruno Poizat, Springer-Verlag, 2000. (A Russian copy of
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
Introduction to Model
Rothmaler, Gordon and Breach Science Publishers, 2000.
Model Theory by C.
Chang and H. J. Keisler,
If you feel adventurous, check
notes (in German!) for a course in model theory taught by Volker
Weispfenning which I wrote a long time ago.
The classical works of Abraham
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.
There will be a problem set due
two weeks or so, to be handed in at the beginning of class. Up to 3
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
1 (due February 6). For solutions click here.
2 (due February 20). For solutions click here.
3 (due March 5). For solutions click here.
4 (due March 29). For solutions click here.
5 (due April 16). For solutions click here.
6 (due April 30). For solutions click here.
below for biographical information about some prominent model theorists:
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