Is the dream solution to the continuum hypothesis attainable?

Details Is the dream solution to the continuum hypothesis attainable? Is the dream solution to the continuum hypothesis attainable?

2012-03-19

arxiv.org/abs/1203.4026v1

Mathematics

Logic

This article is based upon an argument I gave during the course of a three-lecture tutorial on set-theoretic geology at the su

Scientific paper

The dream solution of the continuum hypothesis (CH) would be a solution by which we settle the continuum hypothesis on the basis of a newly discovered fundamental principle of set theory, a missing axiom, widely regarded as true. Such a dream solution would indeed be a solution, since we would all accept the new axiom along with its consequences. In this article, however, I argue that such a dream solution to CH is unattainable. The article is adapted from and expands upon material in my article, "The set-theoretic multiverse", to appear in the Review of Symbolic Logic (see arXiv:1108.4223).

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