Collection Model Theory and Combinatorics
Organizer(s)
Date(s)
26/01/2018
- 02/02/2018
On finite dimensional omega-categorical structures and NIP theories
By Pierre Simon
The study of omega-categorical structures lies at the intersection of model theory, combinatorics and group theory. Some classes of omega-categorical structures have been classified, most notably stable structures of finite rank (following work of Zilber, Cherlin, Harrington, Lachlan, Hrushovski, Evans) and smoothly approximable structures (Kantor–Liebeck–Macpherson and Cherlin–Hrushovski). We conjecture that the class of structures which have polynomially many types over finite sets, which we will call finite dimensional, can also be classified. We will present results that essentially allow to classify the finite rank case, generalizing what is known for stable structures. The main new ingredient comes from the study of NIP theories and involves coordinatizing structures by linear orders.
