Methods in Higher Forcing Axioms: The inevitable conclusion

The meeting in Norwich is over. Here are my thoughts.

It felt haphazard, without a concrete plan. And that was great. In the first day, Tadatoshi Miyamoto and David (Asperó) presented two problems in the morning and in the early afternoon. We then had a discussion about them, and it was just a general discussion, that went very well.

The next day we had a morning that was even less structured, and after lunch Uri (Abraham) gave a presentation of some results in polychromatic Ramsey theory, and suggested problems that might serve as test problems for future developments in higher forcing axioms.

In the last day, we had even more discussions, and in the afternoon we talked about reading material. That part was, to me, the important part of the meeting. We made a list of resources that one can read if one is interested in higher forcing axioms. From blog posts to papers. Some things that should at least be mentioned by name, and some history. I was very happy with the result of that discussion.

In any case, I took notes, but I will only have time to complete them in a few weeks. So the goal is to have them ready and online in early December. Stay tuned for more.

But now let me take a turn and be myself. Let me talk about "the process". It was a small workshop, it was meant as a work-shop, rather than "a small conference". I think that the people who came there learned a thing or two about side conditions and higher forcing axioms, I think we all learned new ideas, and more importantly, I think that this meeting maybe helped pushing this topic a bit further. If nothing else, then at least by making Uri Abraham interested in understanding this topic better.

I wish these kind of meetings would be more ubiquitus in set theory. I think that's a good primer to future research, to future collaborations. Don't force people into lectures and talk on top of a talk on top of another talk on top of a tutorial. Give people time to sit, present a problem, and discuss it. Keep it fluid, keep it dynamic. Change the questions halfway through, if need be. The goal is to generate future work, not to solve something right there and then.

For my money, I am sure that I will organise similar events in the future. I don't know what the topics would be, but I know this was great.

If anyone is also curious, let me give you the gist that should be guiding you when organising this sort of workshop:

1. Picture yourself in a boat, on a river. You're sitting there with the three biggest experts on a topic you're vaguely familiar with, and you ask them a question about some vague idea regarding an open problem. Maybe there's a nice bottle of wine in the boat, or some sandwiches. I don't know, it's your boat and your picture.

2. Limit the number of participants. This is unfortunate, since everyone wants to join everything, more or less, when it's good. But there is something to be said about having about 10 people. We originally expected 10, and we thought we would end up breaking into two groups every day. Due to a last minute cancellation, we were 9, and it seemed to work. I guess it would have been fine with 10 as well, and maybe even 12. But at some point you have less of an all-around discussion, and more of a small group hijacking the time of everyone else. So keep it small, and then you have to make the hard choices, and invite only some of the people you'd have liked to have. Such is life.

3. Prepare a list of questions that people can suggest, refine, improve, and otherwise contribute to.

4. Have people from various levels of "understanding" on the topic. You definitely need someone to ask naive questions, that's important. And you need to have people who feel confident about the topic and the techniqu, but not know everything on the topic either. And of course, you need a few experts.

I'm probably forgetting something. Grab me for a beer next time, and ask me for more advice. And let me know how it all went!