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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeSep 1st 2015
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexI just noticed that Randall Holmes claims to have a [proof](http://arxiv.org/abs/1503.01406) of the consistency of NF. Does anyone know more about this?

   I just noticed that Randall Holmes claims to have a proof of the consistency of NF. Does anyone know more about this?

2. • CommentRowNumber2.
   • CommentAuthorJohn Dougherty
   • CommentTimeSep 1st 2015
   • (edited Sep 1st 2015)
   • PermaLink
   Author: John Dougherty
   Format: MarkdownItexThere was some discussion of the result on the FOM mailing list in [](https://http://www.cs.nyu.edu/pipermail/fom/2013-October/thread.html) [2013](http://www.cs.nyu.edu/pipermail/fom/2013-October/thread.html), then again [in July last year](http://www.cs.nyu.edu/pipermail/fom/2014-June/thread.html).

   There was some discussion of the result on the FOM mailing list in 2013, then again in July last year.

3. • CommentRowNumber3.
   • CommentAuthorZhen Lin
   • CommentTimeSep 1st 2015
   • PermaLink
   Author: Zhen Lin
   Format: MarkdownItexSee also [this MO question](http://mathoverflow.net/questions/132103).

   See also this MO question.

4. • CommentRowNumber4.
   • CommentAuthorDavidRoberts
   • CommentTimeSep 2nd 2015
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexThis has been going on for ages. My guess is that a portion of the difficulty may be arising from the transtranslation from an underlying structural set theory construction to a material interpretation, without never seeing the structural version.

   This has been going on for ages. My guess is that a portion of the difficulty may be arising from the transtranslation from an underlying structural set theory construction to a material interpretation, without never seeing the structural version.

5. • CommentRowNumber5.
   • CommentAuthorMike Shulman
   • CommentTimeSep 2nd 2015
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThanks! I added a comment to [[New Foundations]].

   Thanks! I added a comment to New Foundations.

6. • CommentRowNumber6.
   • CommentAuthorDavidRoberts
   • CommentTimeSep 2nd 2015
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexWhere is it proved that $NFSet$ is not Cartesian closed?

   Where is it proved that $NFSet$ is not Cartesian closed?

7. • CommentRowNumber7.
   • CommentAuthorZhen Lin
   • CommentTimeSep 2nd 2015
   • PermaLink
   Author: Zhen Lin
   Format: MarkdownItexAt least two places: [1](http://www.cwru.edu/artsci/phil/FCCinNF.pdf) [2](https://www.dpmms.cam.ac.uk/~tf/cartesian-closed.pdf).

   At least two places: 1 2.

8. • CommentRowNumber8.
   • CommentAuthorDavidRoberts
   • CommentTimeSep 3rd 2015
   • (edited Sep 3rd 2015)
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexFrom McClarty's article, he is assuming that a pairing operation gives rise to a cartesian product as well as a category with arrows the entire functional relations using said pairing operation. Why not consider the pairing operation as defining a non-cartesian monoidal product and aim for just a closed monoidal category? I guess dropping Cartesianness violates assumption 1 in McClarty's proof and assumption 2 in Forster's proof, so neither apply to show the internal hom can't exist. Clearly we then have to work harder to get existence of limits of various sorts. Also, _some_ binary products may exist, if not all of them. **EDIT:** Hmm, the [recent talk](http://flov.gu.se/english/research/logic/seminar) "A Monoidal Closed Category in NF" by Gorbow [1] seems to establish this result for a slightly larger category of relations, with $Hom(A,B)$ relations on $A\cup B$ (I guess) restricting to functions $A\to B$ as relations from $A$ to $B$. [1] [This](http://www.gu.se/english/about_the_university/staff/?languageId=100001&userId=xgorpa&departmentId=051140) seems to be his university page, but not sure how up to date this is. It seems he is [now in private industry](https://se.linkedin.com/pub/paul-gorbow/16/8b7/137)

   From McClarty’s article, he is assuming that a pairing operation gives rise to a cartesian product as well as a category with arrows the entire functional relations using said pairing operation. Why not consider the pairing operation as defining a non-cartesian monoidal product and aim for just a closed monoidal category? I guess dropping Cartesianness violates assumption 1 in McClarty’s proof and assumption 2 in Forster’s proof, so neither apply to show the internal hom can’t exist.

   Clearly we then have to work harder to get existence of limits of various sorts. Also, some binary products may exist, if not all of them.

   EDIT: Hmm, the recent talk “A Monoidal Closed Category in NF” by Gorbow [1] seems to establish this result for a slightly larger category of relations, with $Hom(A,B)$ relations on $A\cup B$ (I guess) restricting to functions $A\to B$ as relations from $A$ to $B$.

   [1] This seems to be his university page, but not sure how up to date this is. It seems he is now in private industry

9. • CommentRowNumber9.
   • CommentAuthorDavidRoberts
   • CommentTimeSep 3rd 2015
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexI added the references Zhen Lin supplied to the page [[NF]]. It might be worth typing up a sketch of at least McLarty's proof, since it is very short.

   I added the references Zhen Lin supplied to the page NF. It might be worth typing up a sketch of at least McLarty’s proof, since it is very short.