> Gc wrote: > > Aatu Koskensilta kirjoitti: > > > >> No, you're confusing languages and models in some way. A model of set > >> theory is a structure <M,E> where E is a binary relation on M. Such a > >> model is countable if M is a countable set and uncountable otherwise. > > > > If the language is countable, then the model is countable - it has > > countable many elements. > > A model of a countable language may well be staggeringly uncountable.
Yes, I mean by "the model" only the countable model
> > This is just the result. > > No, the result is that every infinite first order model has a countable > elementary substructure.
> > Inside the model > > there is no bijection between real and naturals, but the bijection > > exists between the expressions of the language and the elements. Your > > epsilon- relation stuff doesn`t mean anything outside the model, > > because it doesn`t say anything about the countable language that we > > are dealing with. > > You appear rather badly confused. Just work through Shoenfield and > everything will become clear.
> -- > Aatu Koskensilta (email@example.com) > > "Wovon man nicht sprechen kann, daruber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus