Cofinality spectrum theorems in model theory, set theory and general topology · HackerPapers discussions

Cofinality spectrum theorems in model theory, set theory and general topology — mentioned by clintonc

Wed, 13 Sep 2017 17:40:03 GMT

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)

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Cofinality spectrum theorems in model theory, set theory and general topology — mentioned by v64

Wed, 13 Sep 2017 17:06:16 GMT

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 <= t, and that aleph_1 = p can be shown to imply aleph_1 = t. Note that the inequalities aren't strict inequalities, and this proof is essentially saying that they were equivalent all along. [1] https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_t... [2] https://arxiv.org/pdf/1208.5424.pdf

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Cofinality spectrum theorems in model theory, set theory and general topology — mentioned by xamuel

Wed, 13 Sep 2017 15:39:33 GMT

Actual article: https://arxiv.org/pdf/1208.5424.pdf Great results within a very narrow field, which quantamagazine leverages into a clickbaity title.

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