250073 VO Special Topics in Model Theory (2024S)

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. A modern view holds that model theory is the "geography of tame mathematics" (Hrushovski), with the goal of 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.

This course is a continuation of my class Model Theory from last semester, and will explore more advanced topics. However, I will not assume that you attended the preceding class: a basic knowledge of the language and fundamental results of first-order logic should suffice to successfully follow the class this semester.