Gc wrote: > We know that every set of reals is in some sense countable according to > Skolem`s paradox, I mean that there is a bijection between the real and > naturals if naturals are outside of model of set theory.
We know no such thing. By the Löwenheim-Skolem theorem any model of set theory has a countable elementary substructure. How do you get from this that "every set of reals is in some sense countable"?
> Still Cantor`s > theorem in set theory, which is of course valid, says that the reals > are uncountable. To me it seems that there is a theorem in set theory > that can`t be true in sense I understand you see it. You have said > before that the axioms of set theory are true. How can you explain this > - or am I missing something?
Countable models of set theory are entirely irrelevant to the uncountability of the reals.
-- Aatu Koskensilta (firstname.lastname@example.org)
"Wovon man nicht sprechen kann, daruber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus