Math 223M: Model Theory |

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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.

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:

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.

Other texts on model theory that you might want to consult:

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 Course in Model Theory: An Introduction to Contemporary Mathematical Logic*-
by Wilfrid Hodges, Cambridge University Press, 1997. (See corrigenda.) An expanded version of this book is available under the title Model Theory.*A Shorter Model Theory* -
by Philipp Rothmaler, Gordon and Breach Science Publishers, 2000.*Introduction to Model Theory* -
by C. C. Chang and H. J. Keisler, North-Holland, 1998.*Model Theory* - 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.

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.

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.

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