[FOM] Weak representability as basic?

Panu Raatikainen panu.raatikainen at helsinki.fi
Sat Aug 14 07:23:56 EDT 2010

Dear All

I would be interested in taking a closer look at an approach where one  
takes weak representability (in a formal system) as basic. Recall that  
a set A is weakly represented in a formal system S by a formula F(x) if
    n belongs to A <=> S proves F(n).

(“weakly represent” is also expressed, in the literature, e.g. by  
“represent”, “define”, “weakly define”, and “numerate”.)

Please note that I do *not* want to restrict this to  
Sigma-0-1-formulas, but I want to know about the basic logical  
properties of weak representability by an arbitrary formula.

Does anyone know a more systematic treatment of the notion in the  
literature? Is it studied anywhere for its own sake? In particular, I  
would be interested in the formalization of the whole notion itself in  
a theory of arithmetic, or a theory of formalized metamathematics.

Surely all this should not be too difficult, but I would like to know  
if it is already done somewhere...

All the Best


Panu Raatikainen

Ph.D., Docent in Theoretical Philosophy

Department of Philosophy, History, Culture and Art Studies
P.O. Box 24  (Unioninkatu 38 A)
FIN-00014 University of Helsinki

E-mail: panu.raatikainen at helsinki.fi

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