Scott Mutchnik : The Koponen Conjecture

Posted by Scott Mutchnik , part of the Logic Seminar.

At

Feb. 28, 2024, 4 p.m.

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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.