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@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.

Hmm. That makes me wonder. Can the finite axiomatization of a first-order theory not contain second-order axioms?

> 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?

Jan Van den Bussche refers to it in his paper on the relationship between Tarski's work and database theory:

http://citeseer.ist.psu.edu/vandenbussche01applications.html

The original Tarki paper is reference [52]. Look in Section 5 for a (partial) explanation and some more recent references. Nothing on line as far as I can see, sorry.

Jan Hidders

Received on Thu Sep 16 2004 - 14:27:52 CDT