User blog comment:PsiCubed2/Question: General breakdown of levels up to Second Order Arithmetic/@comment-1605058-20180203222427/@comment-30754445-20180204082949

Wow, that's some rabbit hole I've dragged myself into :-)

Thanks.

I have a couple of more questions:

1. The ordinals in the link you've given are nonrecursive countable ordinals. How do they connect to all this? Isn't the PTO of any theory recursive?

2. What do we have between Πn-reflections and PTO(Π12-CA0)? The "ordinal zoo" link doesn't really help here.