Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?

From: Mike Oliver (mike_lists_at_verizon.net)
Date: 01/27/05 

Date: Wed, 26 Jan 2005 18:23:17 -0600

Daryl McCullough wrote:
> Mike Oliver says...
>>Daryl McCullough wrote:
>>>It doesn't follow from the definition of V that it is a model of ZFC.
>>>It only follows that it is a model of ZF.
>>
>>I think you might have to explain what you mean by that, Daryl.
>>
>>In some sense, all truths about V follow from the definition,
>>by its categoricity: Up to a unique isomorphism there's only
>>one object that answers to the definition.
>
>
> That's what I mean. It isn't that V is defined to be a model of
> ZFC; its definition is the same whether you are working in Z, ZF,
> ZFC, ZFC+GCH, or whatever. It's just that what you can *prove* about
> V is different in these different theories.

Sorry, I still don't see what you're gettng at when you
say it follows from the definition that it's a model of ZF, but
not that it's a model of ZFC. Are you saying nothing more
than that's what follows *from*ZF* ? I thought you had
some deeper point in mind.

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