> Gc wrote: > > Aatu Koskensilta kirjoitti: > > > >> Gc wrote: > >>> Aatu Koskensilta kirjoitti: > >>> > >>>> No, the result is that every infinite first order model has a countable > >>>> elementary substructure. > >>> Yes. > >> So how do you get from this that "every set of reals is in some sense > >> countable"? Why should a model theoretical result about first order > >> logic tell us something about the cardinality of sets of reals? > > > > Because there is a model of set theory which has domain that is > > countable and which I think contains all the reals. > > Well, there isn't. No countable model contains all the reals.
How can the countable model then satisfy all the theorems about the reals?
@xortec.fi) > > "Wovon man nicht sprechen kann, daruber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus