# [FOM] consistency of NF?

Cody Roux cody.roux at andrew.cmu.edu
Tue Jul 1 14:28:24 EDT 2014

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

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

And while I'm on the subject of alternative foundations, what is the
status of Grue's "Map Theory"? Is it decisively equi-consistent with ZFC?

Best,

Cody

On 06/23/2014 03:58 AM, tf at maths.cam.ac.uk wrote:
> On Jun 22 2014, Stephen G Simpson wrote:
>
>> OK Thomas, thank you for that helpful background information.  When
>> you have understood the proof, please post something about it on FOM.
>> While I don't really understand much about NF, it would be nice to
>> know that this long-standing problem has been laid to rest.
>>
>> By the way, what do you mean by "Randall's proof"?  Has he announced a
>> consistency proof for NF?  I must have missed it ....
>
> Oh yes. It's a couple of years old now. He's still tweaking it, which
> is why i haven't yet sat down and got properly stuck into it, tho' two
> of my Ph.D. students are trying to. By the end of my stint in Boise
> both Randall and I should be on top of both proofs.
>
>
>>
>> Best wishes,
>> -- Steve
>>
>> tf at maths.cam.ac.uk writes:
>> > Date: 21 Jun 2014 06:29:44 +0100
>> > > Steve, It's 50-odd pages and i learnt of it only a matter of days
>> ago. > Randall has had a quick look at it and will no doubt reply to
>> this > query. Jamie Gabbay (he is always Jamie, never Murdoch) is a
>> former > student of mine; he has picked up the type theory and NF
>> background - > and of course he knows all the FM stuff from his
>> nominal sets work - so > it is in principle entirely credible that he
>> should find a consistency > proof for NF. I am spending august and
>> september in Boise with Randall > and the project is for me to really
>> understand Randall's proof and - > now! - for us both to understand
>> Jamie's. Watch This Space.
>> > > On Jun 21 2014, Stephen G Simpson wrote:
>> > > >Murdoch Gabbay (http://arxiv.org/abs/1406.4060) has published a
>> proof
>> > >of the consistency of NF.  Has anyone here understood and/or checked
>> > >the proof?
>> > >
>> > >Stephen G. Simpson
>> > >Professor of Mathematics
>> > >Pennsylvania State University
>> > >research interests:
>> > > mathematial logic, foundations of mathematics
>> > >
>> > >_______________________________________________
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>> > >FOM at cs.nyu.edu
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>> > >
>>
>
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