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

Abstract

We connect and solve two longstanding open problems in quite different areas: the model-theoretic question of whether $SO{P}_2$ 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.

60 pages. Editorial and expository changes from previous version. Accepted, Journal of the AMS

References in corpus (1)

• Saturating the random graph with an independent family of small range

Cited by in corpus (3)

• Borel Tukey morphisms and combinatorial cardinal invariants of the continuum
• A parallel to the null ideal for inaccessible lambda. Part I
• Existence of optimal ultrafilters and the fundamental complexity of simple theories