🚀 go-pugleaf

In article <1992Sep7.225943.23043@infodev.cam.ac.uk> gjm11@cus.cam.ac.uk (G.J. McCaughan) writes:
>In article <1992Sep7.062552.21596@guinness.idbsu.edu> holmes@opal.idbsu.edu (Randall Holmes) writes:
>
>> A brief remark:  I do know that the consistency of ZFC is itself open
>> to doubt.  I agree that one can equally well start working in NF with
>> faith in one's heart as we already can in ZFC.  But to start working 
>> in NF, we must give up the Axiom of Choice; this is the real problem
>> from my standpoint.  I have other reasons for doubting the naturalness
>> of NF (but not of NFU) which are not ready for publication.
>
>Hmm. I don't know much about what is and isn't consistent with NF.
>Is Dependent Choice consistent with NF? That would satisfy many of us,
>perhaps including some who don't like the Axiom of Choice in all its
>-- 

The strongest version of Dependent Choice is false in NF, but
there is a weaker version adequate for practical purposes which
appears to be OK.  The problem is that we do not have good techniques
for proving relative consistency results for NF; we do not even know
if denumerable choice or "the real numbers can be well-ordered" are
consistent to adjoin to NF, although we do not see any reason to doubt
this.

-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu