Cofinality Spectrum Theorems in Model Theory, Set Theory and General Topology

We connect and solve two longstanding open problems in quite different areas: the model-theoretic question of whether SOP2 is maximal in Keisler’s order, and the question from general topology/set theory of whether p = 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. Our analysis gives a new characterization of good regular ultrafilters and establishes the existence of a minimum class of non-simple theories in Keisler’s order.