Adding to the excellent paper that Joseph linked:
Is the dream solution to the continuum hypothesis attainable?
Joel David Hamkins
(Submitted on 19 Mar 2012)
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 <http://arxiv.org/abs/1108.4223>).
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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