  We connect and solve two longstanding open problems in quite different areas:
the model-theoretic question of whether $SOP_2$ is maximal in Keisler's order,
and the question from set theory/general topology of whether $\mathfrak{p} =
\mathfrak{t}$, the oldest problem on cardinal invariants of the continuum. We
do so by showing these problems can be translated into instances of a more
fundamental problem which we state and solve completely, using model-theoretic
methods.
