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.
> 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