Methods in Higher Forcing Axioms

Methods in Higher Forcing Axioms (or MEHIFOX, for short) is an experimental workshop hosted in Norwich by David Asperó and myself. You can find the website, right here. This workshop is sponsored by the London Mathematical Society, and the School of Mathematics in UEA.

The idea is to have a workshop, where we actually work. This is contrary to the normal use of "workshop" (in set theory, at least, but I believe in most mathematical areas) which means a very small conference where almost all the participants are also speaking.

We have invited a few people (you can find the list on the site) and we collected a few problems to discuss. The goal is not to solve them, but rather to create strategies and ideas for the solution, and try and promote future collaborations. We will also post on arXiv an informal report containing those ideas, at a later point of time.

One of the reasons I wanted to have a meeting with this format is that research into Higher Forcing Axioms is difficult, it is in its very early stages, and there aren't that many results. We know that just the obvious generalization of properness is not going to work, because club guessing, so there is no simple analogue for PFA, SPFA, or MM.

It is my great hope that this workshop will help us at least organize the existing knowledge. So future researchers will find it easier to get into the field. This, with a tandem work on Higher Baire Spaces, might have interesting results in the future, and if nothing else, will teach us why \(\omega\) is such a special cardinal.

To everyone who follows meetings with the zeal of a true believer, I apologize. I wanted to tell more people about the meeting, I really did. And we did announce it and talked about it, but at the same time, this is an experimental workshop. And if the goal is to do research, then having too many people might end up as counterproductive.

But hopefully, this will go well, and we will learn from it how to organize these kind of events on a larger scale in the future.

In any case, stay tuned for more.