[FOM] Set theology

[joeshipman@aol.com]

Rupert McCallum wrote:

>Well, how about asking "On V_kappa with kappa a measurable, can there
>exist two ultrafilters yielding two distinct theologies?" 

>When the ultrafilter is kappa-complete, easily prove from basic facts
>about measurable cardinals that the "theology" has to be the actual
>theory of V_kappa, so that with this restriction the answer is no.

>Countably complete... unsure at this point.

This is excellent.  It means that if the Universe is measurable, my original proposition holds -- "If the college of cardinals is actually a University, then any Pope it elects is infallible."

Can this be extended to other notions of "election", which do not require an ultrafilter for a class of cardinals to agree on a theology?  

-- Joe Shipman