This is in response to the following quote of Harvey:
Incidentally, do you agree with me that CH research is not a relatively promising area of f.o.m. research? I tend to believe that people think CH research is a promising area of f.o.m. research if and only if they subscribe to “CH has a determinate truth value”.
I am a convinced platonist and fully subscribe to the proposition that CH has a definite truth value.
I am quite sceptical about the prospects of determining CH by any approach currently on the horizon. In particular, I doubt that anything growing out of the work of Sy Friedman or any of the work of Woodin, past or present, that I know about will lead to any determination that I find in the least convincing.
I have enormous respect for Woodin’s mathematical achievements, even though I do not think they have any prospect of leading to a solution of the continuum problem.