Logic Seminar
Scott Mutchnik
UIC
Topic Seminar: Forking
Abstract: We will have a research seminar this semester on forking, broadly construed, particularly in the setting of unstable first-order theories. Graduate students are particularly encouraged to attend.
We will introduce the class of NSOP_1 theories, which contains the class of simple theories while allowing for additional complexity, and to which many of the independence phenomena originating from stable and simple theories extend in new ways. Specifically, Chernikov, Kaplan and Ramsey show that Kim-independence, a version of forking-independence "at a generic scale," behaves similarly in NSOP_1 theories to how forking-independence behaves in simple theories. We will define Kim-independence and give the main ideas of the proofs of some of Kaplan and Ramsey's results on NSOP_1 theories, including Kim's lemma for Kim-dividing, the equivalence of Kim-forking and Kim-dividing, and potentially the symmetry of Kim-independence.
Tuesday September 16, 2025 at 2:00 PM in 427 SEO