Re: The IDS, the EDS and the DBMS
Date: Thu, 16 Sep 2004 14:36:08 -0700
Message-ID: <EUn2d.213$Sp5.117_at_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
> > 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 - 23:36:08 CEST