Is the Dream Solution of the Continuum Hypothesis Attainable?

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.