From: utzoo!watmath!cbostrum
Newsgroups: net.math
Title: Loweheim Skolem
Article-I.D.: watmath.4443
Posted: Mon Jan 31 16:32:44 1983
Received: Mon Jan 31 23:56:57 1983

While we are on the subject of infinity, what opinions are there
on the theorem that says every set of first order axioms in a 
countable language has a countable model?? This makes the people
with big infinities look silly since even if they write down their
set theory axioms and prove that there is an "uncountable set" (so
there are uncountably many objects in their universe), that set
of axioms from which they proved their wondrous result has a countable
model. So where are the uncountable sets, really. (Of course, all they
have proved is that there are infinite sets such that there exists no
1-1 onto corrspondence. THIS DOES NOT ESTABLISH THAT THERE ARE 
UNCOUNTABLE SETS BY ANY MEANS! It just says that what it says.
(I am what I am?)). Comments?