Speaker: Sergei Starchenko
University of Notre Dame
Will give a Logic Seminar entitled:
Ramsey Growth Functions in o-minimal setting
Abstract: Recall that a finite version of Ramsey Theorem states that for any integers k,n there is N such that for any set X of size N, for any coloring of k-element subsets of X, there is a subset $X_0$ of X of size n whose subsets have the same colors. Let’s denote such smallest N by $R_k(n)$. In general the function $R_k(n)$ is an exponential tower of height k. In this talk we consider the case then a coloring is given by an k-ary relation E that is a subset of $\mathbb{R}^k$, definable in an o-minimal structure. We show that if the structure is polynomially bounded, then $R_k(n)$ is at most double exponential. This is a joint work with A.Chernikov and M. Thomas.
Date: 11-19-2024
Time: 2:00 pm
Location: 125 Hayes-Healy Bldg