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

From: Daryl McCullough (stevendaryl3016_at_yahoo.com)
Date: 01/26/05 

Date: 26 Jan 2005 15:00:58 -0800

Mike Oliver says...
>
>Daryl McCullough wrote:
>
>> V is not defined to be a model for ZFC. It is defined to be the
>> class
>>
>> { x | exists an ordinal alpha such that x is in V_alpha }
...
>> 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. 

--
Daryl McCullough
Ithaca, NY

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