FOM: sharp boundaries/tameness

Kanovei kanovei at
Wed Feb 13 12:17:36 EST 2002

>Date: Wed, 13 Feb 2002 10:26:35 -0500
>From: Harvey Friedman <friedman at>

there is no formula of set theory, phi(x), such that ZFC proves

i) there exists a unique x such that phi(x);
ii) x is such a proper elementary extension.

To this statement, can a reference be given? 
A standard Luxemburg construction of a nonmeasurable 
set does not really work in the Solovay model because 
elements of a definable "nonstandard universe" are not 
necessarily themselves definable. 


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