Re: The IDS, the EDS and the DBMS

From: Mikito Harakiri <mikharakiri_at_iahu.com>
Date: Thu, 16 Sep 2004 14:36:08 -0700
Message-ID: <EUn2d.213$Sp5.117@news.oracle.com>

"Jan Hidders" <jan.hidders_at_REMOVETHIS.pandora.be> wrote in message news: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.

>

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

Actually, that extract was pasted from

http://www.nationmaster.com/encyclopedia/real-number

where in the next paragraph we read:

"It is not possible to characterize the reals with first-order logic alone: the Löwenheim-Skolem theorem implies that there exists a countable dense subset of the real numbers satisfying exactly the same sentences in first order logic as the real numbers themselves."

> > 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.

Ah, I remember this reference! But, it doesn't seem to have "real" mentioned anywhere:-( Received on Thu Sep 16 2004 - 16:36:08 CDT