[FOM] CH and forcing

Aatu Koskensilta Aatu.Koskensilta at uta.fi
Tue Jul 5 15:02:13 EDT 2011

Quoting Roger Bishop Jones <rbj at rbjones.com>:

> Consider specifically the interpretation of ZFC consisting of
> all pure well-founded collections of accessible rank.

   Obviously we can't add stuff, e.g. new reals, to <V_kappa,  
epsilon>, with kappa the first inaccessible, and hope this gets us a  
model violating CH. However, there's nothing to stop us starting with  
V_kappa and using the usual machinery of forcing to construct a model  
in which CH fails. It's just that, once all the details are sorted  
out, we find that V_kappa is not a substructure of what we end up  
with, as one might expect based on the usual story. This is a matter  
of putting the oft repeated standard guiding intentions to one side,  
and simply concentrating on the mathematics of it.

Aatu Koskensilta (aatu.koskensilta at uta.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

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