[FOM] S4 + ZFC

Rupert McCallum rupertmccallum at yahoo.com
Thu Aug 23 20:58:29 EDT 2007

--- 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.

Choose the right car based on your needs.  Check out Yahoo! Autos new Car Finder tool.

More information about the FOM mailing list