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.

Prerequisities

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

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.