## Logic Seminar

Scott Mutchnik

UIC

The Koponen Conjecture

**Abstract:**Koponen has conjectured that all simple theories, with quantifier elimination in a finite relational language, are supersimple of finite rank (2016). In particular, she asks whether they are one-based (2014). We discuss our proof of this conjecture, which by Tomašić and Wagner’s results on pseudolinearity (2003), also implies one-basedness. Particularly, we prove that simplicity implies supersimplicity in this setting, thereby highlighting what Kennedy (2020) calls "the fragility of the syntax-semantics distinction.” This is on joint work with John Baldwin and James Freitag.

Wednesday February 28, 2024 at 4:00 PM in 712 SEO