[FOM] Does 2^{\aleph_0} = 2^{\aleph_1}?
joeshipman@aol.com
joeshipman at aol.com
Fri Oct 26 13:01:30 EDT 2007
>Doesn't V=L qualify? Perhaps you meant an axiom consistent with the
negation
>of CH?
>
>James Hirschorn
Yes, I was asking for a natural model in which CH was false and
2^{\aleph_1} was larger than the continuum.
You asked about the result that RVM implies 2^{\aleph_0} =
2^{\aleph_1}. I don't know who first proved this, but the stronger
result that RVM implies no cardinal smaller than the continuum has a
power set larger than the continuum was proved by Prikry (Bulletin of
the AMS 81 (1975), 907-909). You can find a short proof online in
section 5E of Fremlin's monograph "Real-Valued Measurable Cardinals",
which can be downloaded from this page:
http://www.essex.ac.uk/maths/staff/fremlin/rvmc/index.htm
-- JS
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