[FOM] CH and forcing

[Aatu Koskensilta]

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