Why is "0# exists" independent?

martdowd at aol.com martdowd at aol.com
Wed Jul 6 14:38:32 EDT 2022

T. Chow wrote: 

Is there some reason you're asking about "0# exists" as opposed to "V=L"? 
It would seem that the two questions raise similar philosophical issues, 
but isn't the independence of "V=L" an even more basic question?

 "0# exists" is equivalent to uncountable many iindiscernibles.  This implies V\neq L.It occurred to me after I posted my message that the independence of CH is a "hole in ZFC".The question is, why are there holes in ZFC?  Infinitely many indiscernibles seems to beone also.  I was thinking about looking at CH.  There's a Boolean valued model where \neg CHhas nonzero value.  I'm wondering what is provable in ZFC, since the generic model isfictional.  I have to review my basic forcing.
Martin Dowd
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