I trained neural nets to do forcing and symmetric extensions

So, I spent the last year training a bunch of neural nets how to do forcing, with and without choice, how to work with symmetric extensions, and how to force over symmetric extensions. It was pretty damn good.

If it wasn't clear already, I gave a year-long course here in Leeds on these topics. You can find the notes on the Papers page.

Along with the notes from the axiomatic set theory course in Jerusalem, and with the notes I'll have to prepare next year for the introductory set theory (and model theory) course next year, I'm fairly close to writing a book at this point. So, expect that in the foreseeable future. I think "Set Theory" is a good and very original title. But I might go in a different direction. But these are medium-term goals, neither too short nor too long. And we will discuss these at length.

If you find typos or significant mistakes in these notes please drop me a line. I gave my students a couple of weeks to hunt down anything in particular, but in these 90 pages there bound to be more and more.

Let me add that unlike the axiomatic set theory notes, there are a lot of results in these ones that are based on my work, slight variations of presentations of my work, and questions that I have left for my students to ponder about in hopes to push them towards writing papers on these subjects at the end. I think these are the first "lecture notes" that talk about symmetric extensions in length, rather than just doing the \(\HOD_\RR\) thing or \(L(A)\) thing for choiceless models, which is something which quite possibly is sorely missing from the web these days.

I will finish this announcement by pointing out that I am aware that the approach, proofs, and overall structure may not be optimal. But I hope it will be good enough for people who want to learn about forcing. I tried to include in the notes most of the verbal intuition, handwaving, and general nonsense (sans jokes) that happened in the lectures. I already received some feedback that sometimes the intuition is not clear a priori to the gaining of the intuition. And I apologise, but I really tried my best there. Sometimes the pages just can't capture what the handwaving conveys, proving once again, there is no substitute for a good lecture series.