[FOM] Goedel's First Incompleteness Theorem

[praatika@mappi.helsinki.fi]

"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/