Re: The IDS, the EDS and the DBMS
From: Jan Hidders <jan.hidders_at_REMOVETHIS.pandora.be>
Date: Thu, 16 Sep 2004 19:27:52 GMT
Message-Id: <pan.2004.09.16.19.30.51.642372_at_REMOVETHIS.pandora.be>
>
> First order theory of reals would be hardly interested to any real
> matematician (pun intended: real matematician as opposed to logician:-)
> since the center pillar axiom of reals -- the supremum axiom -- refers to
> subsets of the reals and is therefore a second-order logical statement.
Date: Thu, 16 Sep 2004 19:27:52 GMT
Message-Id: <pan.2004.09.16.19.30.51.642372_at_REMOVETHIS.pandora.be>
On Wed, 15 Sep 2004 09:51:35 -0700, Mikito Harakiri wrote:
> "Jan Hidders" <jan.hidders_at_REMOVETHIS.pandora.be> wrote in message
> news:pan.2004.09.15.16.09.04.217597_at_REMOVETHIS.pandora.be...
>> >> The question about the complexity of normalization is also interesting. >> >> From Tarksi we know that the reals are axiomatisable >> > >> > Finitely axiomatisable or not? >> >> Yes, the first order theory of reals is finitely axiomatisable and in fact >> decidable. Ten points if you know why this not contradicts Goedel's >> incompleteness theorems. ;-)
>
> First order theory of reals would be hardly interested to any real
> matematician (pun intended: real matematician as opposed to logician:-)
> since the center pillar axiom of reals -- the supremum axiom -- refers to
> subsets of the reals and is therefore a second-order logical statement.
> As for the ten points, I was unable to google any references to Tarski's
> work on finite axiomatization of reals. Can you please help?
http://citeseer.ist.psu.edu/vandenbussche01applications.html
- Jan Hidders