## Notre Dame Journal of Formal Logic

### Is the Dream Solution of the Continuum Hypothesis Attainable?

Joel David Hamkins

#### Abstract

The dream solution of the continuum hypothesis ($\mathrm {CH}$) 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 $\mathrm {CH}$ is unattainable.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 56, Number 1 (2015), 135-145.

Dates
First available in Project Euclid: 24 March 2015

https://projecteuclid.org/euclid.ndjfl/1427202977

Digital Object Identifier
doi:10.1215/00294527-2835047

Mathematical Reviews number (MathSciNet)
MR3326592

Zentralblatt MATH identifier
1331.03034

Subjects

Keywords
continuum hypothesis multiverse

#### Citation

Hamkins, Joel David. Is the Dream Solution of the Continuum Hypothesis Attainable?. Notre Dame J. Formal Logic 56 (2015), no. 1, 135--145. doi:10.1215/00294527-2835047. https://projecteuclid.org/euclid.ndjfl/1427202977

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