Oh dear! Now fixed.

]]>But now the video is back in place. No longer a howling void.

]]>It then would have to be fractional.

If it was a over b

Then you must see

This could not be actual

For a-square over b-square would equal two

But this certainly would not do

With a bit of effort as we plod

We see a could be neither even nor odd

And this would be counter factual.

This is a great fix, even an improvement in feel — thanks for setting it up!

]]>Oh great! Your belief is right. Thank you!

Okay, such as the Turing Degrees then… Makes me wonder whatis known about universal countable partial orders, more than mutual embeddability… But those two instances plus K.J. Williams’ T-realizations of any countable model of ZFC, already prompts to think they’re even more complicated!

In my paper, which we shall be reading in the seminar in which I believe you are participating this term, I prove that this hierarchy contains copies of the free countable Boolean algebra, and so in particular it is universal for all countable partial orders. So it is very complicated.

]]>Yes, the readings will appear on Professor Halbach’s web page for the course. The seminar is officially for Oxford-affiliated students, but we have made the link public, and so I suppose it is fine to join in, but if there are any problems with this policy we will revise it.

]]>Just wanted to ask you something I did not have time to yesterday: would you have any idea of the order type of the consistency strength order (if ever there are canonically regstered ill-founded & nonlinear order types…)? ]]>

No, this seminar is a discussion style seminar, rather than a lecture, and so we don’t want to record it, so as to encourage student participation as much as possible.

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