# Sean Cox: Coding reals by clubs in $[\omega_2]^\omega$

Speaker: Sean Cox
Institution: Fields Institute
Time: Mon, 10/08/2012 – 4:00pm – 5:30pm
Location: RH 440R

In the 80s Gitik proved the following theorem: For every real $x$ and every club $D \subseteq [\omega_2]^\omega$, there are $a,b,c \in D$ such that $x \in L(a,b,c)$. An immediate corollary of Gitik’s theorem is: if $W$ is a transitive $ZF^-$ model of height at least $\omega_2$ such that $W$ is missing some real, then the complement of $W$ is stationary in $[\omega_2]^\omega$ (Velickovic strengthened Gitik’s Theorem to show that the complement of such a $W$ is in fact projective stationary, not just stationary). I will present Gitik’s proof and, if time permits, discuss some recent applications due to Viale and me.