I went to an interesting maths conference this week (Set theory and its neighbours meets the Cameleon), and I’m probably going to write a report on it at some point. This isn’t that report.
This is just a quick note to say that the stuff about Boolean algebras and operator algebras is at least known, if not well known, and has been for a good few decades. Oh well. The noncommutative stuff probably hasn’t - I’m going to email the guy whose talk was on a related subject and ask him about it.