Re: Godel's Incompleteness and Nonmonotonic Logic

From: Herman Jurjus (h.jurjus_at_hetnet.nl)
Date: 08/26/04 

Date: Thu, 26 Aug 2004 10:24:27 +0200

Aatu Koskensilta wrote:
[snip]

> Second order logic is incomplete in the sense that there is no complete
> deductive system for it, or in other words the second order logical
> consequences of a given second order theory or sentence are not
> recursively enumerable. Gödel's incompleteness theorems do apply to
> second order theories as well in the sense that for all theories
> containing a fragment elementary arithemtic and (sound) deductive system
> there are propositions which are neither refutable nor provable in the
> theory according to the deductive system.

With 'theory' you mean recursively enumerable theory, and for 'deductive
system', a similar restriction is required, i think? 

-- 
Cheers,
Herman Jurjus

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