> > Gc wrote: > > > > > > 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?
Because first-order logic is too weak to tell the difference between the model and the real thing.