Randall Holmes has now announced “I believe that I am in possession of a fairly accurate outline of a proof of the consistency of New Foundations.”

He goes on to say “NF has the same consistency strength as TST + Infinity, has the same kinds of extensions as NFU in the same ways, has no interesting consequences for the combinatorics of small sets, etc. No surprises, this is a rather boring outcome in my opinion …” Well, I don’t know about boring! If Randall has indeed cracked this long-standing problem, it’s a major achievement. He is still editing the document, so nothing is released yet. However, Thomas Forster is organizing a conference here in Cambridge in the spring and Randall says he will “certainly be discussing this.”

And Thomas confirms “I am indeed organising an NF meeting in Cambridge in the spring, current intention is last week of March and first week of April. The idea is that before Randall arrives there will be a warm-up act wherein the background and some preparatory material is set out for people who are not already familiar with it. Thus when Randall arrives we will all be primed and ready to go. … I am not at this stage soliciting other offers of talks, tho’ that may change. If you have something you think I may find irresistible by all means try to twist my arm. And – of course – contact me if you want to come.”

Any speculations about the consistency strength of NF?

Randall says “NF has the same consistency strength as TST + Infinity” … whatever exactly that is! :-)

TST + Infinity has the same consistency strength as bounded Zermelo set theory.

Are there any current (2014) news about the claimed proof?

I believe Randall Holmes is coming to Cambridge around Easter time, and Thomas Forster is planning to lecture here about the proof afterwards. I’ll have more definite news then. I believe the local consensus among those who know about these things is that things are looking good. But I don’t know about when to expect a definitive published version.