Question

Is there research currently being done on ordinals?

Answer 1

I’m not sure it’s exactly *about* ordinals, but there’s a lot of research involving ordinals in proof theory.

Answer 2

Ordinals are fairly well understood. I can't think of any notable open problems off the top of my head.

Answer 3

I’m guessing yes, but I’m not a logician myself. Maybe look at the faculty at U Michigan, U Illinois at Urbana-Champaign, etc, and you might find faculty there who do logic research :)

Probably other schools too, but not sure off the top of my head.