## Posts tagged iterated symmetric extensions

## What a long strange trip it's been...

Apr 25 2017, 09:28

As some of you may have noticed, I don't use this blog to write about my papers in the "traditional way" math bloggers summarize and explain their recent work. I think my papers are prosaic enough to do that on their own. I do use this blog as an outlet when I have to complain about the arduous toil of being a mathematician (which has an immensely bright light side, of course, so in the big picture I'm quite happy with it).

This morning I woke up to see that my paper about the Bristol model was announced on arXiv. But unbeknownst to the common arXiv follower, this also marks the end of my thesis. The Hebrew University is kind enough to allow you to just stitch a bunch of your papers (along with an added introduction) and call it a thesis. And by "stitch" I mean literally. If they were published, you're even allowed to use the published .pdf (on the condition that no copyright infringement occurs).

Continue reading...## Iterating Symmetric Extensions

Jun 22 2016, 07:43

I don't usually like to write about new papers. I mean, it's a paper, you can read it, you can email me and ask about it if you'd like. It's there. And indeed, for my previous papers, I didn't even mention them being posted on arXiv/submitted/accepted/published. This paper is a bit different; but don't worry, this is not your typical "new paper" post.

If you don't follow arXiv very closely, I have posted a paper titled "Iterating Symmetric Extensions". This is going to be the first part of my dissertation. The paper is concerned with developing a general framework for iterating symmetric extensions, which oddly enough, is something that we didn't really know how to do until now. There is a refinement of the general framework to something I call "productive iterations" which impose some additional requirements, but allow greater freedom in the choice of filters used to interpret the names. There is an example of a class-length iteration, which effectively takes everything that was done in the paper and uses it to produce a class-length iteration—and thus a class length sequence of models—where slowly, but surely, Kinna-Wagner Principles fail more and more. This means that we are forcing "diagonally" away from the ordinals. So the models produced there will not be defined by their set of ordinals, and sets of sets of ordinals, and so on.

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