Logic Seminar - George Peterzil

Date: 
Wed, 28/06/202311:00-12:30
Title: Cofinal NIP Families of Finite Sets
Abstract: In their paper, Bays, Ben-Neria, Kaplan and Simon prove that any cofinal family of finite sets on aleph_n has VC dimension at least n+1, and realize this bound for n=1. I will first present these proofs, and later show using forcing that for all n, the bound is consistently tight. Using their work, this gives (the consistency of) new examples of NIP families that cannot be defined in any NIP structure. Time-permitting, I will present a different way to realize the bound in ZFC for n=1, using the forcing-theoretic tools that were developed. 
This work is part of my Master's thesis, done under the joint supervision of Omer Ben-Neria and Itay Kaplan.