Scott Mutchnik : Topic Seminar: Forking

Posted by Scott Mutchnik , part of the Logic Seminar.

At

Oct. 7, 2025, 2 p.m.

In

427 SEO

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 show that the stability of the forking relation, a global variant of the stable forking conjecture, is equivalent for supersimple countably categorical theories to the stable forking conjecture. We then 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.