[FOM] fom: large cardinals and CH

Dave Marker marker at math.uic.edu
Thu Apr 22 12:50:30 EDT 2004

Tim Chow asks:
>Levy-Solovay and Cohen showed that large cardinals cannot be expected to
>settle CH.

>Or so I'm told...I don't understand their work myself.  Could someone
>explain these results in intuitive terms?

The basic idea is that large cardinal notions like "inaccessible",
"measurable" are preserved if we force with a partial order that is
significantly smaller than the cardinal.
For example if we start with a model with a measurable cardinal.
We can force to \aleph_2 Cohen reals and violate CH, or we can
force to collapse the continuum to \aleph_1 and make CH true
while keeping the cardinal measurable.

Dave Marker

More information about the FOM mailing list