[FOM] Continuum Hypothesis

[Mitchell Spector]

On Saturday, May 17, 2003, at 09:35  PM, Harvey Friedman wrote:
> There is no consensus among logicians, and apparently
> not even among set theorists, that anyone has presented
> reasonably compelling axioms that decide CH, or might
> decide CH.

AD implies CH, in the form that every uncountable set
of reals can be placed in 1-1 correspondence with the
set of all reals.

Moreover, the proof uses a method that Cantor would
appreciate, in that every uncountable set of reals
contains a perfect subset.

I think AD can be characterized as "reasonably compelling".

Mitchell Spector
Seattle University
E-mail: spector at seattleu.edu