Xiang Li

Stationary Common Neighbors and Partition Hypotheses

Collapsing a $T^{\kappa^+}_{\omega_1}$-Ramsey cardinal $\kappa$ to $\omega_2$ gives, for every countable coloring of $[\omega_2]^2$, a stationary set $X$ and a color $i$ such that every finite subset of $X$ has stationarily many color-$i$ common neighbors in $X$. The color-$i$ graph on $X$ has diameter at most two afte...