[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
--
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/
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