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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. Wedo so by showing these problems can be translated into instances of a morefundamental problem which we state and solve completely, using model-theoreticmethods.

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