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?