> 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. There is therefore somekind of unformal bijection between the reals and natural numbers and I would like to now a theory which says it. If there is no somekind of unformal bijection between naturals and reals, i don`t understand why is it called Skolem`s paradox and what that last quote that I posted is talking about bijections outside the model and stuff.
> -- > Aatu Koskensilta (firstname.lastname@example.org) > > "Wovon man nicht sprechen kann, daruber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus