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Re: Is it sure that any mechanism has a largest model? (LI,8C, p.205)



What is a "countable infinity"?
 
Secondly: If you have a finite set of models, and each intersection of models constitutes another model, you will end up with a really huge number of models, but it would still be a finite set, would it not? Because you would exhaust the number of different combinations, eventually, before repeating them.
 
On the other hand, an infinite set of models will always be infinite.


Boris: Nevertheless, don't you think we still need to proove that the infinite intersection of models is still a model?

TG: Hmmm.....I am not sure. I think if we agree that the intersection of any finite number of models is a model, then by induction so will the intersection of an infinite number of models....at least when it is a countable infinity.

I will have to think about this some more. At the moment, I cannot think of stronger reasoning than that.