Is the dream solution to the continuum hypothesis attainable?
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).
- Publication:
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arXiv e-prints
- Pub Date:
- March 2012
- DOI:
- 10.48550/arXiv.1203.4026
- arXiv:
- arXiv:1203.4026
- Bibcode:
- 2012arXiv1203.4026H
- Keywords:
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- Mathematics - Logic;
- 03Exx;
- 03Axx
- E-Print:
- This article is based upon an argument I gave during the course of a three-lecture tutorial on set-theoretic geology at the summer school "Set Theory and Higher-Order Logic: Foundational Issues and Mathematical Developments", at the University of London, Birkbeck in August 2011