250119 VO Model theory (2021W)

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 will serve as a first introduction to this multi-faceted subject. Both the development of general theory and some applications (mainly to algebra) will be presented.