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arXiv · 1203.4026

Is the dream solution to the continuum hypothesis attainable?

Joel David Hamkins
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Abstract

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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Joel David Hamkins. 2012-03-19. Is the dream solution to the continuum hypothesis attainable?. https://doi.org/10.1215/00294527-2835047

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