It's great that Scott is having his stab at solving the exposition problem for the Continuum Hypothesis. I'm looking forward to the future parts of the series!
The Continuum Hypothesis is also very interesting because it is a poster child in a discussion between adherents of the "traditional dream solution" of the Continuum Hypothesis and the intriguing "multiverse philosophy of set theory". In short, the former is the attempt to devise new axioms which would settle the hypothesis. The latter is the position to embrace all possible mathematical universes.
The Continuum Hypothesis is also very interesting because it is a poster child in a discussion between adherents of the "traditional dream solution" of the Continuum Hypothesis and the intriguing "multiverse philosophy of set theory". In short, the former is the attempt to devise new axioms which would settle the hypothesis. The latter is the position to embrace all possible mathematical universes.
I tried to give an exposition of that circle of ideas here: https://iblech.gitlab.io/bb/multiverse.html Comments and questions are very welcome.