Math 506: Model Theory

General Information

Time and Place: MWF 11-11:50am, 300 Lincoln Hall
Control Number: 06882

Instructor: Matthias Aschenbrenner
E-mail address: e-mail
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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Click here to download the class information handout.


An introduction to model theory, emphasizing both general theory and applications to algebra. Specific topics to be covered include:

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 good general reference for mathematical logic is Mathematical Logic by Joseph R. Shoenfield, A K Peters, Ltd., 2000.

The classical works of Abraham RobinsonIntroduction 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 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.