[FOM] S4 + ZFC

[Rupert McCallum]

--- Michael Carroll <mcarroll at pobox.com> wrote:

> The modal system S4 has been used meta-theoretically in the study of
> set 
> theory and the independence proofs (Smullyan & Fitting, "Set Theory
> and the 
> Continuum Hypothesis", for example). From a formal standpoint, it
> would then 
> seem natural to ask: what happens if we add modal operators to the
> object 
> language of ZFC (or NBG), and adjoin the S4 axioms as logical axioms?
> Do the 
> incompleteness proofs remain unaffected by this change?
> 

Surely conservativity is obvious. Just get rid of all the boxes.



       
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