[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  

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 Raatikainen

Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy

Department of Philosophy
University of Helsinki

E-mail: panu.raatikainen at helsinki.fi


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