[FOM] Weak representability as basic?

[Panu Raatikainen]

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


-- 
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
Finland

E-mail: panu.raatikainen at helsinki.fi
http://www.mv.helsinki.fi/home/praatika/