Strong Erdos Hajnal in VC minimal theory

Title:  Strong Erdos Hajnal in VC minimal theory

Speaker:  Yayi Fu (Notre Dame)

Abstract:  We will show that if $T$ is a VC minimal theory (e.g. ACVF) and $M\models T$, then for any $d$ and any definable relation $E(x,y)\subseteq M^2$ of complexity $\leq d$ in Swiss Cheese decomposition, there is $k_d>0$ such that for any disjoint finite $A,B\subseteq M$, there exist $A'\subseteq A$, $B'\subseteq B$ with $|A'|\geq k_d |A|$, $|B'|\geq k_d |B|$ such that $A'\times B' \subseteq E$ or $A'\times B'\subseteq\neg E$.