This talk is about some cardinal invariants related to $\omega_1$. The antichain number is the least cardinal for which there does not exist a subcollection of that size with pairwise finite intersections, and the matching number is the least cardinal for which there exists a subcollection X of that size of order-type $\omega$ subsets of $\omega_1$ so that every uncountable subset of $\omega_1$ has infinite intersection with a member of X. We explore how these invariants behave in various forcing extensions. Joint work with Geoff Galgon.