## Louise Hay Logic Seminar

Roland Walker

UIC

Externally Definable Sets and Shelah Expansions

**Abstract:**A major focus of model theory is the study of definable sets. In this talk we will discuss externally definable sets and Shelah expansions. Our goal will be to prove a theorem of Saharon Shelah stating that in the NIP setting, Shelah expansions have quantifier elimination. While proving the theorem, we will review and use several basic techniques involving quantifier-free types, heirs, coheirs, and coheir sequences. We will also discuss some areas of open research concerning externally definable sets.

Thursday September 22, 2016 at 4:00 PM in SEO 427