Jonathan Schilhan (Leeds)

Strong almost disjointness

A collection of unbounded subsets of $\omega_1$ is strongly almost disjoint if each pairwise intersection is finite. I will present Baumgartner's thinning out technique and use it to show that under Martin's Axiom + "failure of weak CH" every $\omega_1$-mad family has an $\omega_1$-mad strongly almost disjoint refinement. My presentation will be a mix between lecture and research talk. It has come to my ears that students of set theory in Leeds have not learned about $\Delta$-systems. For this reason I will present this powerful combinatorial result which is the essence of most ccc proofs. All subject to my bad management of time.