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.
Continuing from last time (when we motivated the shift from local to global versions of the stable forking conjecture), we will discuss the simple Kim-forking conjecture in NSOP_1 theories, and prove cases of this conjecture from joint work with Baldwin and Freitag, including an infinite-variable global variant in a general NSOP_1 theory, a finite-variable global variant in the case of finite F_Mb, and the full conclusion of the simple Kim-forking conjecture, given enough indices, for forking with realizations of an isolated type with the definable Morley property. All three of these results use a strong version of Kim’s lemma in NSOP_1 theories, due to Kaplan and Ramsey, which says that all Kim-independent Morley sequences exhibit Kim-dividing.
Tuesday October 14, 2025 at 2:00 PM in 427 SEO