Math 223M: Model Theory

General Information

Time and Place: MWF 2-2:50pm, Mathematical Sciences Building 7608

Instructor: Matthias Aschenbrenner

E-mail address:

Mathematical Sciences Building 5614
Office Phone: (310) 206-8576
Office Hours: MWF 1-2pm, or by appointment.

Achtung!Reading files from this website requires software to display PDF files, such as Acrobat Reader or Ghostview.

Click here to download the original course announcement.


Model theory is a branch of mathematical logic which applies the methods of logic to the study of mathematical structures, and thus has impact on other parts of mathematics (e.g., number theory, analytic geometry). Since its beginnings in the early decades of the last century, the perception of what the subject is about has gone through various incarnations. Because many of the mathematical structures studied in model theory have an algebraic origin, Chang and Keisler (1973) simply decreed that universal algebra + logic = model theory, whereas Hodges (1993) defined model theory more broadly as the study of the construction and classification of structures within specified classes of structures. A modern view holds that model theory is the geography of tame mathematics (Hrushovski). Here, the emphasis is on identifying those classes of structures whose first-order theories can be understood (in some well-defined technical sense), and exploiting such an understanding as a tool in other parts of mathematics.


Basic knowledge of first-order logic (Math 220), especially the completeness theorem and elementary set theory, and abstract algebra (Math 210), especially field theory.


Review of structures and theories. Quantifier elimination, model completeness. Types, saturation, omitting types. Totally transcendental theories, strong minimality, Morley's Theorem. Some o-minimality (time permitting).

Course Text

I will follow my own notes, but the following book will be a good companion for this course: Model Theory: An Introduction by Dave 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 an occasional problem set assigned every two weeks ago, which will be handed out in class, and will also posted on this website. Solutions are due in class on the date specified on the homework sheet.

Back to my homepageBack to my home page.      BauarbeitenLast modified March 30, 2009.