Adding to the excellent paper that Joseph linked:


 Is the dream solution to the continuum hypothesis attainable?

Joel David Hamkins <http://arxiv.org/find/math/1/au:+Hamkins_J/0/1/0/all/0/1>
(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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