# [FOM] consistency of NF?

Randall Holmes holmes at diamond.boisestate.edu
Fri Feb 25 15:39:34 EST 2005

Dear FOM'ers,

I am looking for refutations of a purported proof of the consistency
of NF, which is found at the head of the Current Research section of
my web page

http://math.boisestate.edu/~holmes/holmes/nfconsistency.ps

This is a quite brief argument, but it does require one to read a (very
nice) paper of Marcel Crabb\'e:

Marcel Crabb\'e, The
Hauptsatz for comprehension, a semantic proof'', {\em Mathematical
Logic Quarterly\/}, 40 (1994), 481-489.

in which he proves cut-elimination for NF with no extensionality axiom.
It appears to me at the moment that with a slight additional twist this
can be turned into an NF consistency proof.

While I believe this at the moment, I certainly don't quite meta-believe
it, so I await refutation with interest.

--Randall Holmes