  These notes are based on Appalachian Set Theory lectures given by M.
Malliaris on November 5, 2016 with D. Casey as the official scribe. The aim of
the lectures was to present the setup and some key arguments of "Cofinality
spectrum problems in model theory, set theory and general topology" by
Malliaris and Shelah. This provides a sketch of the proof that $\mathfrak{p} =
\mathfrak{t}$ and that $SOP_2$ theories are maximal in Keisler's Order.
