Proving GCH

After a morning disrupted by an early migrain messing up my visual cortex, I ought really to have taken things easy, but something quite entertaining has just happened.

I'll bore you with the chain of events.

First, I have to get my mail fixed, it just stopped yesterday and raising a ticket didn't get it fixed. However, the support guys pointed out that the mail was reaching my mailboxes on the server so it was just the collection which was awry. I found that one account was working, compared its configuration in my client with my main non-working account, noticed a difference and brought them into line. That fixed the problem. Some software which used to accept both ways of configuring the accounts had been upgraded, and no longer supported them both.

So now my mail downloads, and in there is a call for participation in the "Trusted extensions to ITPs" workshop. This reminds me of the last one, in which I had a lengthy disagreement with a logician from MIT (several disagreements, but one in particular) who insisted that it could be proved that all models of set theory have the same structure of ordinals. I insisted they don't all have the same height. After the workshop it occurred to me that he must have been talking about INNER models.
Which do have the same height because its part of the definition that they have "all" the ordinals.
(which is relative to the interpretation of the meta-language).

So the call for participation has got me thinking about set theory.

Now the entertainment. Within minutes I have a "proof" of GCH (the Generalised Continuum Hypothesis)! So it seems.
Must be wrong of course, we know it can't be done don't we?

Well it is a bit of philosophy rather than a bit of mathematics, I know its not provable in any accepted axiomatisation of set theory.

Still, I believe I have a proof, which is really entertaining (if you like that kind of thing), and so I will have to write it up and see what objections people can find to it.
This will be a bit like my proof that V does not exist (if its good).
You post to FOM and some people have a go at trashing it for a while, and fail, and then everything calms down and people carry on as if it had never happened.
Though a convincing proof of GCH would be harder to ignore than one that V does not exist, the consequences of which are more subtle.

So the next stage is to write it up, formalise what can be formalised, and see whether I still believe it.

RBJ