[FOM] Rosser sentences

[praatika@mappi.helsinki.fi]

Just a spontaneous thought I did not reflect that carefully (so feel free 
to give criticism):

I wonder whether one could use the length of a proof instead of the size of 
its godel number to have a rosser-like sentence which is not depended on a 
particular godel numbering?  At first sight, this seems to make the 
sentence Pi-0-2, not Pi-0-1, but I wonder whether one can get around this...
Intuitively, it seems to me that the resulting property is nevertheless co-
r.e. (i.e. Pi-0-1).


(Whether or not this is relevant: most actual godel numberings seem to have 
the property that 
     length(p1) < length(p2)   =>  gn(p1) < gn(p2)   
and
     gn(p1) < gn(p2)  =>    length(p1)<_ length(p2).
(p1, p2 are proofs, gn's their godel numbers). 
I wonder whether one could somehow utlize this issue?) 

If anything like this is definitely impossible, I would be interested in 
seeing clearly why exactly. 

Best

Panu


Panu Raatikainen

PhD., Docent in Theoretical Philosophy
Fellow, Helsinki Collegium for Advanced Studies
University of Helsinki
 
Address: 
Helsinki Collegium for Advanced Studies
P.O. Box 4
FIN-00014 University of Helsinki
Finland

E-mail: panu.raatikainen at helsinki.fi
 
http://www.helsinki.fi/collegium/eng/Raatikainen/raatikainen.htm