[FOM] consistency of NF?

[tf at maths.cam.ac.uk]

On Jul 3 2014, Cody Roux wrote:

>Just to be clear, with respect to what are they showing consistency of NF?

 At this stage, it's ZF, but it's a pretty safe bet that, when the smoke 
and dust have cleared, we should be able to do it relative to Zermelo set 
theory. (That's Holmes' proof i have in mind, but i think the two proofs 
are very closely related. Ask me in october after i have spent 6 weeks in 
conclave with Holmes going over both proofs)

>What is the strongest system known to be consistent conditional on 
>consistency of NF?

Roland Hinnion wrote a thesis about this in the 1970's, and there is a 
translation of it linked from my home page. The answer - at this stage - is 
MacLane set theory (with infinity) Hinnion calls this theory Z\Delta_0 
F\Delta_0 os something like that, but it's nowadays just called Mac.

         tf

www.dpmms.cam.ac.uk/~tf