[FOM] Goedel's First Incompleteness Theorem
praatika@mappi.helsinki.fi
praatika at mappi.helsinki.fi
Sun Oct 25 11:37:12 EDT 2009
"David F. Isles" <david.isles at tufts.edu>:
> I would appreciate it if someone could mention a survey or listing of
> different proofs of Goedel's First Incompleteness Theorem.
The following might be helpful:
Kotlarski, Henryk "The incompleteness theorems after 70 years." Ann.
Pure Appl. Logic 126 (2004), no. 1-3, 125-138.
A general warning: often the "different proofs" establish something
much more local and weaker than Gödel's theorem, e.g. just the
incompleteness of PA, and not the incompleteness of *any* consistent
formal system which contains elementary arithmetic, as Gödel's theorem
does.
And to prove that, the (more-or-less) original Gödel-Rosser proof may
still be - if not the only - at least the simplest way. (There are
obviously some variations around)
All the Best,
Panu
Panu Raatikainen
Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy
Department of Philosophy
University of Helsinki
Finland
E-mail: panu.raatikainen at helsinki.fi
http://www.mv.helsinki.fi/home/praatika/
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