Cofinality spectrum theorems in model theory, set theory, and general topology

Abstract

We connect and solve two long-standing open problems in quite different areas: the model-theoretic question of whether S O P 2 SOP_2 is maximal in Keisler’s order, and the question from general topology/set theory of whether p = t \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.