How the continuum hypothesis could have been a fundamental axiom
Joel David Hamkins
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Abstract
I describe a simple historical thought experiment showing how we might have come to view the continuum hypothesis as a fundamental axiom, one necessary for mathematics, indispensable even for calculus.
arXiv comments
19 pages. Commentary can be made on the author's blog at https://jdh.hamkins.org/how-ch-could-have-been-fundamental. v2 includes many minor improvements, as well as new discussion of several issues, including the fact that ZFC proves (without CH) that there is a unique initial countably saturated real-closed field
The pdf file is available at: https://arxiv.org/pdf/2407.02463
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