[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
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