[FOM] The semantics of set theory

Kanovei kanovei at wmwap1.math.uni-wuppertal.de
Mon Oct 7 08:48:51 EDT 2002

>From rds at logic.univie.ac.at Mon Oct  7 08:40:41 2002
Date: Mon, 7 Oct 2002 08:38:44 +0200 (CEST)

I guess I misunderstand you, as otherwise you'd be wrong.
It is possible to define "x is a true statement of set theory"
in a language which has class variables. The point is that we 
can intend the class variables to range just over predicative 
classes as we can prove all instances of the Tarski schema in
the theory BGC. (Generalizations of this are in an old paper
of mine.) The idea of course is simply that x is true iff 
it belongs to a class which contains only truths; however, if
x is \Sigma_n then the canonical recursively defined such class
is \Sigma_n as well (for n>0), hence predicative. --Best, Ralf  

Yes you clearly misunderstand the point. 
In your "definition" above  x is just a free variable, 
n is a term depending on x, 
therefore, your reference to Sigma_n 
as a sourse of predicativity just is wrong. 



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