November 22
Alex Kruckman,
Wesleyan University
A diversity of Kim's Lemmas
One of the most important steps in the development of simplicity theory by Kim and Pillay in the 1990s was a result now known as Kim's Lemma: In a simple theory, if a formula divides, then this dividing is witnessed by every Morley sequence in the appropriate type. More recently, variants on Kim's Lemma have been shown (by Chernikov, Kaplan, and Ramsey) to follow from, and in fact characterize, the combinatorial dividing lines NTP2 and NSOP1: two generalizations of simplicity in different directions. After surveying the Kim's Lemmas of the past, I will speculate about a new combinatorial dividing line, generalizing both NTP2 and NSOP1 and characterized by a new variant of Kim's Lemma. This is joint speculation with Nick Ramsey.