Nick Ramsey : Binarity, Treelessness, and Generic Stability

Posted by James Freitag , part of the Logic Seminar.

At

Nov. 1, 2022, 4 p.m.

In

636 SEO

Abstract

A theory T is called binary if any two tuples have the same type if and only if all corresponding subtuples of length 2 have the same type. With this strong restriction on theories, it turns out that certain classification-theoretic dividing lines collapse: for example, we show that a binary NSOP_1 theory is simple, and a binary NSOP_3 theory is NTP_1. Motivated by these results, we develop the basics of neostability theory for the broader category of treeless theories. We show such theories come equipped with a natural notion of independence, defined in terms of generically stable partial types, which is meaningful in both simple and NIP theories. This is joint work with Itay Kaplan and Pierre Simon.