Re: [HM] Question regarding Dedekind and numbers
Carlos Cesar de Araujo (lavarini@digitus.com.br)
Fri, 23 Apr 1999 03:11:56 -0300
I appears that Richard Grandy, like many mathematicians, failed to
understand the tremendous difference between a first-order axiom system
and a second-order axiom system. The axiom system to which Dirk Schlimm
refers is of second-order because of the supremum axiom (every
non-empty set of real numbers which has an upper bound must have a least
one). Any two models of such a second-order axiom system are isomorphic;
there is no contradiction here with the Lowenheim-Skolem theorem. By the
way, see also the enter "Categorical axiom system" in
http://members.aol.com/jeff570/mathword.html. On the other hand, I am
very, very interested in Bettazzi's proof. Could Walter Felscher talk
something more about it?
Carlos Cesar