User blog:PsiCubed2/Question: General breakdown of levels up to Second Order Arithmetic

In the last month I've been researching the professional literature on this. Most of it went way over my head, but one thing gave me hope: It seems like a well-explored territory. The feat of reaching PTO(Z2) may still be beyond the reach of professionals, but they clearly have a detailed map for getting their.

So I want to ask the professionals here a few questions:

1.What does the ordinal landscape up to PTO(Z2) looks like? Can you provide a list of the most important milestones up to PTO(Z2)?

I know that something called Π-reflections come to play at the relatively early stage, that Π2-reflections correspond to I, Π3-reflections correspond to K, and "Πω-reflections" (technically wrong notation but you get the meaning) correspond to something called "stable ordinals".

So what comes next?

2. What do these "reflections" actually mean anyway?

3. I've noticed that the literature never talks about Π1-reflecting ordinals. Why is that?

Thanks in advance to all those who answer.