FOM: forcing and Quine's NF holmes at
Tue Mar 28 13:42:31 EST 2000

Dear All,

The march of progress has made something I said on this list
recently outdated:

Holmes said:

The situation for NFU is entirely different; it supports basically the
same technology for relative consistency and independence proofs that
standard set theory (ZFC) supports (plus the techniques that work in
NF!).  For example, one can do forcing in NFU.  (Actually, one can do
forcing in NF as well, but the forcing construction creates
urelements, so one cannot build models of NF with desired properties
- -- one can prove consistency of extensions of NFU in NF using forcing,
which is not what one really wants).

Holmes corrects himself on basis of new evidence:

It appears that one can do independence proofs by forcing in NF
+ Rosser's Axiom of Counting.  This is a new development.  I'll
put some notes about it on the New Foundations home page (accessible
from mine) if it holds up on further examination.

And God posted an angel with a flaming sword at | Sincerely, M. Randall Holmes
the gates of Cantor's paradise, that the       | Boise State U. (disavows all) 
slow-witted and the deliberately obtuse might | holmes at
not glimpse the wonders therein. |

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