Gc wrote: > Aatu Koskensilta kirjoitti: > >> Countable models of set theory are entirely irrelevant to the >> uncountability of the reals. > > I don`t understand how, if what Shoenfield says is true.
In the passage you quoted Shoenfield explains how a first order theory in which the formalization of "there is an uncountable set" is provable can have countable models. From this it does not follow that "every set of reals is in some sense countable".
-- Aatu Koskensilta (email@example.com)
"Wovon man nicht sprechen kann, daruber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus