arXiv:1208.5424math.LO
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 $SOP_2$ 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.
Actual article: https://arxiv.org/pdf/1208.5424.pdf Great results within a very narrow field, which quantamagazine leverages into a clickbaity title.
xamuelView on HNParent context
Disclaimer: I have a math background, but this isn't my field. The continuum hypothesis was proved to be independent of ZFC. From glancing at the first few paragraphs of the actual paper [2], it's been established for decades that the following inequality holds: aleph_1 <= p <=…
v64View on HNParent context
p and t are implicitly defined cardinalities (i.e., the smallest cardinalities with given properties). See Definition 1.1 of the source article (https://arxiv.org/pdf/1208.5424.pdf)
clintoncView on HNParent context