[FOM] S4 + ZFC
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
> 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
> 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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