[FOM] New Foundations consistency problem

[T.Forster at dpmms.cam.ac.uk]

The proof as it stands is relative to ZFC but this is overkill. The idea 
seems to be that, properly optimised, it will show that NF is consistent 
relative to Simple Type theory (or Mac Lane set theory) plus infinity, 
which would confirm an old hunch of Boffa. Thus NF would not prove the 
existence of sets of size aleph_omega.


On Oct 27 2013, WILLIAM TAIT wrote:

> Can you say relative to what the consistency is proved or claimed to be 
> proved? E.g.is Con(NF) claimed to be a theorem of ZFC?
>
>Bill
>
>On Oct 24, 2013, at 1:18 AM, T.Forster at dpmms.cam.ac.uk wrote:
>
>> Randall Holmes has a proof of Con(NF). It's a very complex object, and 
>> he redesigns it every now and then with a view to making the 
>> construction clearer, so it's very much a moving target. My Ph.D. 
>> students and i are gradually working our way through it. The view here 
>> is that it is all true, but it's going to be months before we're 
>> confident that we are on top of it.
>> 
>> 
>> On Oct 24 2013, Alasdair Urquhart wrote:
>> 
>>> I wonder if anybody could tell me the current status
>>> of the consistency problem for NF?
>>> 
>>> 
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