[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 
>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:


-- JS

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