[FOM] Rosser sentences

praatika@mappi.helsinki.fi praatika at mappi.helsinki.fi
Fri Jul 18 10:42:41 EDT 2003

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)   
     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. 



Panu Raatikainen

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

E-mail: panu.raatikainen at helsinki.fi


More information about the FOM mailing list