FOM: V=L and large sets

Kanovei kanovei at
Sat Apr 29 05:12:25 EDT 2000

>Date: Fri, 28 Apr 2000 08:58:10
>To: fom at
>From: Colin McLarty <cxm7 at>
>Subject: FOM: V=L and large sets

>I believe you can say in ZFC: "o is an ordinal and the set
>V(o) has a forcing extension which models ZFC+(there is a measurable)" 

This you can say (you have just said it by an entirely 
legitimate sentence in the language of ZFC), but perhaps 
this is not what you are looking for. Indeed L does not 
have any generic extension with measurable cardinals, 
even if some o in L *is* a measurable cardinal in a 
(necessarily non-generic) extension of L. 


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